THREE-PHASE    TRANSMISSION 


Overhead  Line  for  100,000  Volts,  showing  Transposing  Towers. 


[THREE-PHASE 


TRANSMISSION 


ipractical  {Treatise 


ON  THE   ECONOMIC   CONDITIONS   GOVERNING    THE 

TRANSMISSION  OF  ELECTRIC  ENERG  Y 
BY    UNDERGROUND    AND    OVERHEAD    CONDUCTORS 


BY 

WILLIAM    BREW,    M.I.E.E. 

i\ 

LATE  CHIEF   EXPERT-ASSISTANT,    DUBLIN   CORPORATION    ELECTRICITY   SUPPLY 


NEW   YORK 
D.    VAN    NOSTRAND    COMPANY 

23  MURRAY  AND  27  WARREN  STREETS 

LONDON 

CROSBY     LOCKWOOD     AND     SON 
1911 


PREFACE 


WITH  the  increasing  range  of  literature  designed  to  meet  the 
requirements  of  the  electrical  student,  engineer,  and  specialist, 
some  explanation  may  perhaps  be  offered  for  the  appearance 
of  a  book  devoting  itself  almost  entirely  to  the  electrical  trans- 
mission of  energy  by  three-phase  currents. 

That  this  system  of  transmission  is  eminently  suited  to 
modern  requirements  is  obvious  from  the  fact  that,  with  the 
extended  application  of  electricity  to  industrial  purposes,  under- 
takings formerly  distributing  single-phase  or  continuous  current 
have  alike  resorted  to  three-phase  transmission  in  order  to 
enable  them  to  cope  with  their  widening  field  of  operations. 
Thus  with  the  very  general  use  of  three-phase  transmission  the 
practical  consideration  of  the  subject  in  all  its  bearings  has 
become  of  the  greatest  importance. 

Most  engineers  concerned  with  the  generation  and  distribu- 
tion of  electrical  energy  have  from  time  to  time  met  difficulties 
involving  financial  and  other  considerations,  which  many  text- 
books, excellent  in  other  respects,  have  ignored  completely, 
whereas  the  importance  of  sound  financial  principles  in  all 
technical  questions  cannot  be  overestimated. 

It  appeared,  therefore,  there  was  a  want  of  a  practical 
treatise  upon  the  subject  of  three-phase  transmission  with 
definite  aims  in  view.  In  the  first  place,  to  bring  prominently 
before  the  reader  such  economical  and  financial  points  as 
engineers  and  specialists  engaged  upon  new  works  would  find 
useful  ;  in  the  second  place,  to  provide  the  earnest  student 
with  concrete  examples  of  problems  which,  whilst  demanding 
scientific  treatment,  are  yet  dependent  upon  commercial  con- 
siderations for  their  useful  solution. 


vi  Preface 

Accordingly,  in  the  following  pages,  the  endeavour  has  been 
made  to  keep  constantly  in  view  the  all-governing  question  : — 
Will  it  pay  ? 

Whilst  some  knowledge  of  electrical  engineering  on  the  part 
of  the  reader  is  assumed,  mathematics  have  been  omitted  as  far 
as  possible,  and  where  algebraical  expressions  are  introduced 
these  are  of  the  most  elementary  character. 

References  also  have  for  the  most  part  been  omitted  as 
uninteresting  to  the  general  reader  and  involving  an  amount 
of  labour  and  research  incommensurate  with  their  utility  to 
practical  engineers. 

The  book  contains  some  original  investigation  and  much 
data  not  hitherto  published,  which,  it  is  hoped,  may  prove  of 
interest. 

In  conclusion,  the  author  desires  to  express  his  indebtedness 
to  Dr  W.  E.  Sumpner  for  valuable  suggestions,  also  to  Messrs 
The  British  Insulated  &  Helsby  Cables  Ltd.  ;  Ferranti  Ltd.  ; 
Maschinenen-fabrik  Oerlikon,  Reyrolle  &  Co.  Ltd. ;  and  to  the 
Council  of  the  Institution  of  Electrical  Engineers,  for  details  and 
illustrations  of  plant  kindly  furnished  by  them.  Much  credit  is 
also  due  to  the  publishers  for  the  pains  they  have  taken  to 
make  the  book  perfect  in  every  respect. 

W.  B. 

LONDON,  January  1911. 


CONTENTS 


CHAPTER    I 

PAGES 

INTRODUCTORY  1-16 

E.H.P.  Trunk  Mains  of  Extensive  Schemes— Electrical, 
Financial,  and  Legal  Considerations — Supplementary 
Supply— Special  Features  of  Overhead  Transmission. 


CHAPTER    II 

TRANSMISSION  LOSSES        -  17-41 

Copper,  Dielectric,  and  Sheath  Losses  under  Working  Con- 
ditions— Influence  of  Board  of  Trade  Regulations — Type 
of  E.H.P.  Generating  Plant,  &c. — Conditions  Governing 
Maximum  Economy  with  any  Load  Curve— Kelvin's  Law 
versus  Exigencies. 

CHAPTER    III 

WORKING  PRESSURE  42-58 

Limiting  Values  with  Underground  Mains — Breakdown 
Strength  of  Paper  Insulated  Cables  —  Variation  of 
Dielectric  Strength  with  Temperature — Relation  of 
Working  Pressure  to  Dielectric  Loss — The  "Corona" 
Effect  with  Bare  Conductors — Variation  of  Generator 
Pressure  with  Power  Factor  of  Load — Capacity  and 
Self-induction  of  Line. 

CHAPTER    IV 

THE  CONTROL  OF  E.H.P.  TRUNK  MAINS  59-90 

Switchboard  Construction — Time  Element  Relays  and  Auto- 
matic Oil  Switches —Precautions  necessary  with  Time 
Element  Switches — Reverse  Power  Relays  on  Trunk 
Mains  in  Parallel — Conditions  Governing  the  Overload 
Setting  of  Automatic  Switches — Safety  of  Cables  under 
Switching  Operations — Merz-Price  Protective  Gear. 


Vlll 


Contents 


CHAPTER    V 

IMPEDANCE,  HARMONICS,  &c.  91-122 

Impedance  of  Three  and  Four  Core  Cables— Pressure  Rise 
from  Resonance — Power  Surges — Reflected  Waves,  &c. — 
Effects  of  Odd  Harmonics  on  Plant  Connected  to  Trunk 
Mains. 

CHAPTER   VI 

EARTHING     -  -     123-136 

General  Considerations — Resonance  Phenomena  in  Earth  Wire 
— Electrostatic  Methods  of  Testing  Insulation  on  E.H.P. 
Systems — Pressure  Effects  upon  Unearthed  Systems  of 
Mains. 

CHAPTER    VII 

LINE  APPLIANCES    -  -    137-160 

Supports— Telephones — Lightning  Arresters— Choking  Coils 
— Power  Factor  Correction — Boosting. 

APPENDIX  161-174 

Regulations  Regarding  Overhead  Lines — Numerical  Cal- 
culations by  Symbolic  Method — Miscellaneous  Formula? 
— Self- Induction  and  Capacity  of  Wires. 

INDEX          -  -     175-178 


THREE-PHASE    TRANSMISSION 


CHAPTER    I 
INTRODUCTORY 

IN  the  present  work  the  writer  proposes  to  discuss  from  the 
station  engineer's  standpoint  the  subject  of  three-phase  power 
transmission,  in  connection  with  which  huge  sums  of  money 
have  been  sunk  in  the  past,  and  much  larger  sums  will  pro- 
bably be  expended  in  the  future  with  the  natural  growth  of 
transmission  schemes  and  the  extended  distribution  of  elec- 
tricity for  power,  lighting,  and  traction  purposes. 

The  trunk  mains  of  the  future  within  the  United  Kingdom 
will,  according  to  the  present  tendency,  largely  consist  of 
E.H.P.  three-phase  armoured  cables  laid  underground,  although 
it  is  well  known  that  an  overground  line  can  generally  be 
constructed  from  about  half  to  one-third  of  the  capital  this 
involves.  We  may,  however,  see  trunk  mains  of  overground 
type  more  extensively  adopted  in  the  future. 

The  conditions  to  be  met  by  the  electrical  transmission  and 
distribution  of  power  vary  considerably  in  different  countries. 
In  England  the  problem  usually  resolves  itself  into  the  supply 
of  energy  in  bulk  to  numerous  consumers  within  compara- 
tively small  areas  densely  populated  and  within  which  coal  is 
abundant.  Accordingly,  the  use  of  overhead  transmission  lines 
is  somewhat  restricted,  and  the  distribution  of  energy  has  to 
be  effected  by  means  of  more  expensive  underground  cable 
systems. 

With  transmission  schemes  abroad  in  countries  where  coal  is 
scarce,  and  districts  are  sparsely  populated,  it  is  often  economical 
to  transmit  power  over  very  great  distances  by  means  of  over- 
ground lines  between  water-power  sources  of  energy  and  towna 


2  Three-Phase  Transmission 

or  cities  within  which  the  energy  is  utilised  for  tramways, 
lighting,  or  industrial  purposes.  Accordingly,  the  working 
pressures  in  use  on  Continental  and  American  transmission 
schemes  greatly  exceed  those  in  use  anywhere  within  the 
British  Islands.  An  inspection  of  the  following  tables,  giving 
particulars  of  some  British  and  foreign  transmission  schemes, 
will  at  once  render  this  evident.  It  will  be  seen  that  whereas 
the  highest  working  voltage  generally  in  use  in  England  is 
20,000  volts,  some  Canadian  and  American  schemes  are  using 
pressures  as  high  as  1 10,000  volts.  Moreover,  whilst  the 
maximum  distance  over  which  energy  is  at  present  transmitted 
in  England  does  not  generally  exceed  20  or  30  miles,  we  find 
energy  transmitted  over  distances  of  300  miles  abroad. 

It  is  of  interest  to  note,  however,  that  both  in  the  United 
Kingdom  and  abroad  it  is  becoming  common  practice  to  link  up  a 
number  of  generating  stations  to  the  same  network  of  trans- 
mission lines  whether  these  consist  of  overhead  wires  or  under- 
ground cables  or  a  combination  of  both,  and  this  has  become  a 
distinguishing  characteristic  of  the  Power  Companies  in  England 
working  under  special  Act  of  Parliament  over  large  areas,  as 
compared  with  the  more  numerous  Companies  and  Municipal 
Authorities  working  under  Provisional  Orders  within  strictly 
confined  areas. 

The  linking  up  of  a  number  of  power  stations  to  the  same 
network  of  mains  in  the  North  of  England  has  enabled  power 
running  to  waste  in  the  form  of  gas  from  coke  ovens,  &c.,  to  be 
utilised.  Such  waste  heat  stations  are  installed  at  a  number 
of  points,  and  these  are  linked  up  to  the  steam-driven  stations, 
which  only  supply  the  deficit  of  power  required  to  meet  the 
demand  from  consumers  at  any  time. 

On  similar  lines  abroad,  water  power  and  steam-driven 
auxiliary  stations  are  linked  up  to  the  same  network,  the  steam- 
driven  stations  being  used  during  the  shortage  of  water  which 
occurs  at  definite  periods  of  the  year  in  the  case  of  many  rivers. 
An  interesting  example  of  such  a  system  is  to  be  found  in  the 
South  of  France  where  one  company,  the  Societe  Energie 
Electrique  du  Littoral  Mediterranean,  supplies  direct  256  town- 
ships and  indirectly  a  further  83  townships  including  ten  tram- 
way systems. 

The  synchronising  of  the  various  generating  stations  on  the 
same  H.T.  network  and  over  great  lengths  of  transmission  lines 


Varying  Requirements  3 

has  presented  no  difficulty,  the  impedance  of  the  line  in  fact 
being  found  beneficial  in  keeping  down  the  amount  of  the 
synchronising  current. 


TABLE  I. — OVERHEAD  TRANSMISSION  SCHEMES  ABROAD. 


Undertaking. 

Maximum 
Transmission 

Maximum 
Load  in 

Maximum  Length 
of  Transmission, 

Voltage. 

Kw. 

Miles. 

Hydro-Electric  Power  Com- 

110,000 

310 

mission,  Canada 

Spanish  Hydro-Electric  Co. 

66,000 

25,000 

1  60 

Spokane,  Washington 

6o,OOO 

8,000 

100 

La  Plombiere,  France                           57,ooo 

3,000 

124 

Californian  Gas  and  Electric              55,ooo 

T54 

Corporation 

700  total 

Gaucin,  Seville 

52,000 

3,900 

78 

Vizzola  Campocologno,  Nor- 

45,000 

36,000 

" 

thern  Italy 

TABLE  II. — UNDERGROUND  AND  OVERHEAD  TRANSMISSION 
SCHEMES — BRITISH. 


Undertaking. 

Maximum 
Transmis- 
sion Volt- 
age. 

Maximum 
Load  in 
Kw. 

Maximum 
Length  of 
Transmis- 
sion, Miles. 

1 
Remarks. 

Newcastle  -  upon  -  Tyne 

20,000 

37,880 

15 

Electric  Supply  Co. 
Cleveland  and  Durham 

2O,OOO 

24,400 

1  5 

Electric  Power  Co. 

County     of     Durham        20,000 

23,370 

15 

Electric  Power  Co. 

Clyde    Valley    Electric       11,000 

19,000 

32 

20  miles  overhead. 

Power  Co. 

North         Metropolitan 

I  I,OOO 

1O,OOO 

16 

Electric  Power  Sup- 

ply Co. 

Yorkshire           Electric 

10,000 

10,000 

21 

Power  Co. 

South    Wales    Electric 
Power      Distribution 

11,000 

6,150 

25 

90    miles    under- 
ground ; 

Co. 

9  miles  overhead. 

Lancashire         Electric 

10,000 

5,300 

12 

60    miles    under- 

Power Co. 

ground  ; 

14  miles  overhead. 

4  Three-Phase  Transmission 

The  extended  use  of  E.H.P.  underground  cables  involves 
some  special  considerations  of  an  electrical,  financial,  and  legal 
nature,  regarding  which  little  appears  to  have  been  written  up 
to  the  present,  and  a  brief  review  here  of  some  of  these  may 
prove  of  interest  to  practical  engineers. 

Electrically,  we  have  questions  of  the  most  suitable  voltage 
for  transmission  with  these  cables  under  various  conditions ;  the 
possible  economies  to  be  effected  in  working  as  regards  copper, 
dielectric,  and  sheath  losses  ;  some  sorely  needed  reforms  in 
controlling  switchgear ;  and  methods  of  insulating  at  cable 
receivers,  switches,  and  instrument  connections ;  and  quite  a 
number  of  other  points. 

Financially,  we  have  had  before  us  in  the  past  the  phenomen- 
ally high  price  of  copper  and  the  possibility  of  this  high  price 
again  holding,  combined  with  a  dear  money  market 

Legally,  we  have  the  requirements  of  the  Board  of  Trade, 
the  Home  Office  statutory  obligations,  and,  in  the  case  of 
municipal  undertakings,  the  requirements  of  the  Local  Govern- 
ment Board  also  to  meet. 

In  contemplating  any  extensions  to  plant  or  mains,  the 
engineer  has  usually  one  or  more  of  the  following  considerations 
before  him : — 

1.  The  urgency  of  the  work  necessary  to  cope  with  increasing 
business  or  of  maintaining  the  continuity  of  the  supply. 

2.  The  limits  of  the  extension  advisable  to  be  taken  in  hand 
immediately  as  influenced   by  the  rate  of  growth   of  business 
on  the  one  hand  and  the  favourable  or  otherwise  condition  of  the 
metal  and  money  markets  on  the  other  hand. 

3.  Economies  to  be  effected   by  the  substitution  of  modern 
and  efficient  plant  for  obsolete  plant,  and  the  financial  soundness 
of  the  change  as  shown  by  the  saving  to  be  effected  and   its 
ability  to   meet  the   annual    charges   of  both   existing   capital 
commitments  and  of  the  capital  required. 

4.  The  enthusiasm  or  push  factor  of  the  promoters  of  rival 
methods  of  illumination,  traction,  or  power,  and  the  inevitable 
disaster   resulting   from    a  sitting-still    policy  common    to   any 
commercial  undertaking. 

The  scope  of  the  present  chapter  will  only  permit  of  a  brief 
discussion  of  items  Nos.  2  and  3  above. 

With  regard  to  I,  however,  it  may  be  said  that  the  statutory 
obligations  of  a  Corporation  or  Power  Supply  Company  may 


Financial  Considerations 


demand  the  first  steps  being  taken  irrespective  of  financial  or 
other  considerations.  An  emergency  may  require  the  engineer 
to  decide  things  quickly,  and  may  not  permit  of  the  careful 
weighing  up  of  all  considerations  which  should  influence  his 
decision  towards  the  best  end  being  achieved.  A  valuable  asset 
in  such  cases  is  undoubtedly  engineering  instinct,  provided  it  is 
successful.  Few  committees  or  boards  of  directors  are  humane 
in  the  case  of  failure. 

With  regard  to  2,  it  will  be  convenient  for  reference  in  what 
follows  if  we  review  briefly  at  this  point  some  financial  considera- 
tions generally  affecting  extensions  to  electricity  undertakings. 

Taking  the  case  in  which  a  Municipal  Authority  is  the  under- 
taker ,  it  is  to  be  noted  that  the  Local  Government  Board  in 
sanctioning  loans  for  municipal  trading  apparently  allow  the 
following  periods  for  their  repayment,  such  periods  being  supposed 
to  represent  the  life  of  the  various  sections  of  the  plant.  The 
corresponding  depreciation  has  been  added  on  the  assumption 
that  the  annual  instalments  are  invested  at  3  per  cent,  com- 
pound interest : — 

TABLE  III. 


Life-Years.            Depreciation  at 

3  per  cent.  C.  1. 

Engines    - 

15                            5-37 

Dynamos 
Switchboards    - 

20                            3.74 
25                            2.74 

Cables  laid  solid 

25                            2.74 

Cables  armoured 

'5                        5-37 

Transformers    - 

ID                          5-37 

Buildings 

50 

0.89 

Land 

60 

0.44 

Borrowing  powers  having  been  sanctioned  by  the  Local 
Government  Board  with  due  regard  to  the  existing  obligations  of 
the  municipality  and  to  the  rates  not  proving  an  undue  burden 
to  the  citizens,  the  Municipal  Authority  may  obtain  a  loan  from 
the  Treasury  or  in  the  open  market  at  current  rate  of  interest. 

The  effect  of  the  period  for  which  a  loan  is  granted,  and  the 
rate  of  interest  at  which  it  can  be  obtained  upon  the  annual 
repayments  required  for  every  ,£100  borrowed,  are  shown  by  the 
following  table : — 


Three-Phase  Transmission 

TABLE  IV. 


Annual  Repayments  Covering  Interest  and  Sinking  Fund. 

Years  of 

Loan. 

At  3!  per  cent. 

At  4  per  cent. 

At  4^  per  cent. 

At  5  per  cent. 

10 

12 

12.3 

12.6 

13.0 

15 

8-7 

9-0 

9-3 

9.65 

2O 

7.0 

7-35 

7.65 

8.0 

25 

6.07 

6.42 

6.77 

7.12 

30 

5-4 

5-75 

6.1 

6.5 

35 

5.0 

5-37 

5-74 

6.15 

It  may  be  mentioned,  however,  that  should  the  money 
market  quotations  be  abnormally  high  at  a  time  it  is  necessary 
to  effect  a  loan,  powers  are  sometimes  given  to  extinguish  the 
loan  at  the  end  of  five  years  or  other  period  by  the  raising  of 
a  further  loan  upon  more  advantageous  terms ;  the  new  loan 
in  such  cases  being  granted  for  the  remaining  number  of  years 
covered  by  the  original  loan. 

As  an  example  of  one  of  the  considerations  governing  an 
extension  may  be  mentioned  the  laying  down  of  additional 
cables,  when  trenches  are  open,  before  they  are  actually  wanted, 
which  will  often  effect  economy  in  trenching  and  reinstatement, 
and  avoid  the  obstruction  of  busy  thoroughfares  a  second  time.  It 
is  only  proper,  however,  that  in  avoiding  such  obstruction  the 
cost  of  doing  so  should  in  every  case  be  considered. 

During  1905,  with  copper  bars  at  £76  per  ton  and  lead 
at  .£13.8  per  ton,  the  cost  of  a  0.15  three-core  6,000  volt  cable 
laid  and  jointed  in  cast-iron  trough  was  approximately  ,£1,180 
per  mile.  In  1907,  with  copper  bars  at  £122  per  ton  and  lead 
at  £22.5  per  ton,  the  cost  of  the  same  cable  laid  and  jointed 
in  cast-iron  troughs  was  approximately  ^1,560  per  mile.  The 
cost  of  trenching  and  reinstatement  did  not  alter  appreciably 
within  this  interval,  and  for  a  single  or  double  trough  trench 
30  inches  deep  in  first-class  setts  may  be  taken  as  costing 
approximately  £528  per  mile.  That  is  to  say,  £528  per  mile 
would  have  been  saved  in  trenching  and  reinstatement  if  two 
cables  had  been  laid  in  1905  upon  the  supposition  that  the 
second  cable  would  not  be  required  until  1907,  two  years  later. 
Had  a  Municipal  Authority  been  the  undertaker,  interest  and 
sinking  fund  in  accordance  with  the  usual  practice  would  have 


Financial  Considerations  7 

had  to  be  provided  upon  the  capital  represented  by  the  cost  of 
the  second  cable  during  the  two  years  it  was  entirely  unproduc- 
tive. In  the  case  of  a  company,  however,  the  charges  to  revenue 
during  the  two  years  considered  would  have  been  limited  to 
depreciation  alone. 

In  1905,  loans  for  twenty-five  years  were  granted  to  Municipal 
Authorities  at  3^  per  cent,  corresponding  to  an  annual  payment 
for  interest  and  sinking  fund  of  approximately  6  per  cent,  of 
the  capital  borrowed.  In  the  example  before  us,  therefore,  with 
an  unproductive  capital  amounting  to  £1,180  per  mile  of  cable 
sunk  for  two  years,  the  charge  to  revenue  would  have  amounted 
to  £141.6.  On  the  other  hand  we  should  have  effected  an 
economy  of  ,£528  on  account  of  trenching  and  reinstatement, 
leaving  a  saving  of  £386.4  per  mile. 

The  above  example,  however,  does  not  take  into  account 
three  other  very  important  factors.     These  are : — 
(a)  The  variation  of  the  money  market, 
(£)  The  variation  of  the  metal  market, 
(c)  Depreciation, 

during  the  period  of  two  years  considered.  For  instance,  loans 
were  obtainable  on  a  twenty-five  years'  basis  in  1907  at  about 
4|  per  cent. 

The  rise  in  the  price  of  metals  increased  the  price  of  the 
cable  from  £1,180  to  £1,560  per  mile  during  this  period. 

The  depreciation,  in  the  ordinary  sense,  of  the  cable  was 
discounted  by  the  enhanced  value  of  the  metals  used  in  its 
construction. 

Taking  into  account  the  variations  which  occurred  during 
the  two  years  considered,  a  Municipal  Authority  putting  down 
an  extra  cable  in  1905  would  have  made  annual  repayments 
for  interest  and  sinking  fund  during  the  twenty-five  years'  life 
of  the  cable,  amounting  in  all  to  about  £1,770  per  mile.  Had 
it  deferred  putting  down  the  cable  till  wanted  in  1907  and  raised 
a  loan  then  for  the  purpose,  the  total  repayments  on  account 
of  same  during  its  life  of  twenty-five  years  would  have  amounted 
in  all  to  about  £2,640,  a  difference  of  £870,  which,  added  to  the 
saving  in  trenchwork  of  £386.4,  represents  a  total  saving  of 
£1,256.4,  i.e.,  more  than  the  entire  cost  of  the  extra  cable 
itself  if  laid  in  1905. 

The  scope  of  the  present  chapter  will  not  permit  of  carrying 
this  point  further,  but  the  example  given  will  show  the  import- 


Three-Phase  Transmission 


ance  of  considering  the  extensions  of  an  undertaking  side  by 
side  with  the  prices  holding  in  the  money  and  metal  markets 
respectively. 

With  regard  to  item  No.  3  and  the  replacement  of  obsolete 
or  inefficient  plant  by  other  of  modern  and  more  economical 
type,  Municipal  Authorities  are  very  much  in  the  hands  of  the 
Local  Government  Board  in  this  respect,  who  may  or  may  not 
grant  a  fresh  loan  until  the  original  loan  obtained  upon  the 
obsolete  plant  has  been  paid  off;  and  unless  the  electricity 
undertaking  is  in  the  fortunate  position  of  having  a  reserve  fund 
put  by  out  of  revenue  to  cover  depreciation  and  obsolescence  it 
may  be  saddled  with  inefficient  plant  until  it  has  run  its  natural 
life  and  the  full  interest  and  sinking  fund  instalments  have  been 
paid. 

As  an  example  illustrating  this  point,  we  may  take  trans- 
formers. In  1902  the  average  price  of  a  100  k.w.  oil-cooled 
E.H.P.  transformer  was  approximately  .£100,  and  the  average 
magnetising  loss  on  open  circuit  of  this  size  of  transformer  about 
1,200  watts.  In  1907,  in  spite  of  the  increased  value  of  copper, 
the  average  price  for  this  size  and  type  of  transformer  remained 
approximately  the  same,  but  the  magnetising  losses  of  some 
of  the  best  types  were  as  low  as  450  watts  and  averaged 
600  watts.  A  loan  obtainable  in  1902  at  3!  per  cent,  interest 
would  represent  an  annual  charge  to  revenue  of  £8.7  per  ;£ioo 
borrowed  on  the  basis  of  a  fifteen  years'  life.  On  the  other  hand 
loans  effected  in  1907  at  \\  per  cent,  would  represent  an  annual 
charge  to  revenue  of  £9.3  per  £100  borrowed.  Now  in  order  to 
arrive  at  a  financial  result  we  shall  require  to  know  the  value 
of  the  magnetising  units  in  each  case. 

Assuming  the  old  transformers  to  be  scrapped  and  new  ones 
substituted  the  annual  charges  to  revenue  will  stand  as  follows  : — 


loo  Kw.  TRANSFORMER,  1902. 

Interest      and      Sinking 

Fund        -        -        -        -    /; 


£87 


100  Kw.  TRANSFORMER,  1907. 
Interest  and  Sinking  Fund — 


New  Transformer 
Old  Transformer 


£9.3 

8.7 


In  the  case  considered  it  will  be  found  that  for  the  number  of 
magnetising  watts  required  by  the  new  and  old  transformers,  i.e., 
600  and  1,200  respectively,  it  will  pay  to  entirely  scrap  the  old 


Supplementary  Supply  9 

transformers  if  the  cost  per  unit  of  magnetising  energy  exceeds 
0.42  5  d. 

With  regard  to  consideration  No.  4,  it  will  be  unnecessary 
to  discuss  at  length  the  various  rivals  to  the  applications  of 
electricity  in  its  various  branches.  The  keen  competition  of 
high-pressure  incandescent  gas  lamps  is  now  being  met  with 
flame  arc  lamps  and  metallic  filament  glow  lamps.  The  com- 
petition of  petrol-driven  vehicles  must  be  met  by  efficiently 
operated  electric  tramways,  and  the  competition  of  isolated 
steam,  suction  gas,  and  other  plants  by  electric  power  supply 
undertakings  designed  and  worked  upon  a  thoroughly  sound 
financial  basis.  The  developments  of  each  competitor  must  be 
carefully  and  closely  watched  and  kept  ahead  of  by  the  electrical 
undertaking  in  its  business  capacity,  its  extensions  and  develop- 
ments in  every  direction. 

This  brings  us  to  the  consideration  of  a  state  of  affairs  which 
has  sometimes  arisen  in  recent  years,  and  which  may  prove 
competition  of  a  serious  nature  to  an  existing  electricity 
undertaking,  or  may,  on  the  other  hand,  prove  of  material 
assistance,  according  to  circumstances,  that  is,  the  possibility  of 
a  supplementary  electricity  supply  being  given  by  a  Power 
Company  situated  without  an  area  already  served  by  an  existing 
electricity  undertaking. 

In  the  event  of  an  undertaking  serving  a  definite  area  finding 
it  desirable  from  want  of  capital,  space  for  extension,  or  other 
reasons  to  supplement  the  supply  of  energy  to  its  existing 
cable  system  by  purchasing  energy  from  an  outside  source,  it  is 
apparent  that  to  obtain  the  full  benefit  of  the  dual  supplies  they 
should  be  capable  of  being  worked  in  parallel,  if  discontinuity 
is  to  be  avoided  whenever  change-over  operations  become 
necessary.  In  view  of  the  many  uses  to  which  electricity  is 
now  put,  and  which  demand  absolute  continuity  in  the  supply, 
such  interruptions  as  would  be  involved  by  changing  over 
operations  without  paralleling  could  generally  not  be  tolerated 
upon  an  extensive  system. 

In  considering  the  feasibility  of  parallel  working  between 
the  Power  Company's  system  and  the  city  supply  system,  we 
are  met  with  such  considerations  as  the  synchronising  of  the  two 
systems,  the  maintenance  and  sharing  of  the  load  between  them 
in  due  and  proper  proportion,  and  the  combined  regulation  of 
pressure  at  the  city  end  of  the  Power  Company's  line. 


IO 


Three-Phase  Transmission 


If  we  assume  certain  substations  within  the  city  area  are 
allocated  to  the  Power  Company  to  deal  with,  it  will  probably 
first  be  necessary  that  the  line  pressure  of  the  Power  Company 
be  transformed  to  a  pressure  corresponding  to  that  adopted 
upon  the  existing  high-pressure  feeders  in  connection  with  the 
city  substations,  to  render  the  dual  supply  available,  and 
secondly,  transformed  within  the  substations  to  the  correct 
pressure  in  ordinary  use  by  the  existing  consumers.  As  to 
whether  the  Power  Company  can  under  these  conditions  give 
a  supplementary  supply  upon  the  same  basis  as  the  City 
Authority  will  depend  upon  the  relative  cost  per  unit  of 
electrical  energy  delivered  to  the  distributing  network  by  the 
City  Authority  and  Power  Company  respectively. 

Bearing  in  mind  that  areas  allocated  to  the  Power  Company 
would  in  general  be  outlying  districts,  the  load  factor  may 
possibly  be  of  a  low  order.  If  due  to  a  lighting  load  pure  and 
simple,  we  may  assume  a  load  factor  of,  say,  13  to  14  per 
cent. 

Now  the  all-day  efficiency  of  transformers  working  upon 
an  extensive  private  lighting  system  with  a  load  factor  of 
13  per  cent,  was  found  to  be  87  per  cent.,  that  is  to  say  of  the 
total  number  of  units  per  annum  reaching  the  city  from  the 
Power  Company's  station,  13  per  cent,  would  be  accounted  for 
in  iron  and  copper  losses  in  the  transformers  if  it  was  necessary 
to  convert  the  supply  to  the  working  pressure  of  the  existing 
substations.  In  addition  to  this  loss  there  is,  of  course,  the 
transmission  loss  to  be  taken  into  account.  We  have,  therefore, 
also  to  determine  what  the  annual  loss  in  the  line  would  amount 
to  under  the  conditions  of  the  load  factor  assumed.' 

With  the  lighting  load  curves  referred  to  having  an  average 
load  factor  of  13  per  cent,  for  summer  and  winter,  it  was  found 
that  the  square  root  of  the  mean  square  value  of  the  load 

current  throughout  the  year  was  very  closely  a  third,  i.e.,  —  —  of 

the  maximum  current  in  the  same  interval.     Using  this  value 
we  can  now  arrive  at  figures  for  annual  transmission  loss  given 
the  maximum  load  current  and  resistance  of  the  line. 
For  example  assume  : — 

Voltage  of  transmission  =  20,000  volts. 
Drop  in  line  at  full  load  =  8  per  cent. 


Technical  Considerations  n 

Then  we  get : — 

Annual  transmission  loss  2.48  per  cent. 

Annual  transformation  loss  13.0          „ 

I5-48        ,, 


In  the  above  example  it  is  obvious  that  the  Power  Company 
could  profitably  supply  the  City  Undertaking  upon  its  existing 
basis  of  cost  per  unit  if  their  own  costs  per  unit  were  more  than 
15  per  cent,  below  those  of  the  City  Undertaking  under  the 
working  conditions  assumed. 

There  are  so  many  technical  points  of  difference  between 
the  transmission  of  power  by  overhead  conductors  and  by 
underground  cables,  that  it  may  be  advisable  to  review  some 
of  the  more  important  of  these  briefly  at  this  stage  before 
discussing  them  in  closer  detail  later  on  where  analogous 
considerations  arise  with  underground  cables.  We  may  review 
these  conveniently  under  the  following  headings : — 

Working  Pressure 

Impedance  and  Capacity. 

Maximum  Economy. 

Protection  from  Lightning. 

Working  Pressure. — Up  to  the  beginning  of  1908  line 
insulators  of  pin  type  were  largely  in  use  in  America  and  on 
the  Continent  with  working  pressures  limited  to  about  60,000 
volts.  About  this  time  the  suspension  type  of  insulator  came 
into  use,  consisting  of  porcelain  discs  about  10  in.  in  diameter 
suspended  one  below  the  other.  The  number  of  discs  required 
in  series  depends  upon  the  line  pressure,  each  disc  being 
nominally  capable  of  resisting  a  pressure  of  from  25,000  to 
30,000  volts  (Fig.  i). 

With  this  type  of  insulator,  the  pressure  which  can  be  used 
upon  the  transmission  line  is  only  limited  by  the  formation  of 
the  "  corona  "  or  brush  discharge  from  the  wires,  which  occurs 
at  what  is  called  the  critical  voltage  and  depends  upon  the 
diameter  of  the  wires,  their  distance  apart,  atmospheric  con- 
ditions, &c. 

The  loss  of  power  which  occurs  from  atmospheric  dispersion 
after  the  critical  voltage  is  reached  becomes  very  heavy,  accor- 
dingly, this  point  has  become  of  primary  importance  in  the 
design  of  high-pressure  transmission  schemes. 


12 


Three-Phase  Transmission 


With  a  line  pressure  of  between  1 50,000  and  200,000  volts  it 
would  appear  that  the  limit  has  been  reached  in  the  voltage 
which  can  be  employed  on  overhead  lines  using  bare  conductors, 
unless  the  wires  are  of  abnormally  large  diameter  or  some  special 
insulating  covering  be  applied  to  the  conductors  to  prevent  the 
formation  of  the  "corona"and  consequent 
heavy  loss  of  power  in  transmission. 

Impedance   and    Capacity.  —  The 

impedance  of  the  overground  line  will 
be  directly  affected  by  the  spacing  of  the 
wires  and  the  frequency  adopted  with 
the  system.  The  charging  or  capacity 
current  of  the  line  will  be  proportional 
to  the  working  pressure,  the  frequency 
of  the  system,  and  will  also  depend  upon 
the  spacing  of  the  line  wires. 

The  spacing  of  the  wires  varies  some- 
what with  different  schemes.  In  the  case 
of  the  50,000  volt  lines  in  the  South  of 
France  the  line  wires  are  spaced  5  ft.  9  in. 
apart.  In  America  spacings  of  7  ft.  and 
10  ft.  are  common.  A  spacing  of  10  ft. 
between  wires  would  appear  to  be  as 
great  as  can  be  efficiently  adopted  in 
most  cases,  owing  to  the  fact  that  the  self- 
induction  of  the  line  becomes  of  import- 
ance in  increasing  the  reactance  drop  and 
reducing  the  power  factor  of  the  system. 
This  will  be  seen  from  an  inspection  of  the  following  table  : — 

TABLE  V. — THREE  oooo  S.W.G.  WIRES  CARRYING  100 
AMPERES  100  MILES  AT  FREQUENCY  =  60  CYCLES. 


FIG.  i. 


Distance  between 
Line  Wires. 

C.R.  Drop  per 
Line  Wire. 

Inductive  Drop  per 
Line  Wire. 

Total  Drop  between 
Line  Wires. 

Inches. 

Volts. 

Volts. 

Volts. 

36 

3,367                             6,560 

12,730 

48 

3,367 

7,020 

13,50° 

70 

3»367 

7,430 

14,130 

120 

3,367 

8,  1  80 

15,350 

Technical  Considerations  13 

The  general  practice  is  to  run  two  lines  of  three  wires  each, 
one  set  on  each  side  of  a  steel  lattice  work  tower  suspended  by 
means  of  three  cross  arms.  Typical  arrangements  are  shown  in 
Figs.  2  and  3. 

The  frequencies  most  usually  adopted  on  the  Continent  are 
25  and  50  cycles,  and  in  America  either  25  or  60  cycles.  The 
use  of  the  higher  frequencies  on  long  transmission  lines  is 
accompanied  by  largely  increased  reactive  drop  on  the  line,  and 
also  a  proportionate  increase  in  the  charging  current. 


TABLE  VI. — CHARGING  CURRENT  AT  60  CYCLES  OF  100 
MILES  OF  THREE-PHASE  LINE  oooo  S.W.G.  WIRES. 


Pressure  between 
Line  Wires. 

Distance  between 
Line  Wires. 

Charging  Current 
in  Amperes,  per 
Line  Wire. 

Apparent 
Kilowatts. 

Volts. 

Inches. 

10,000 

36 

7-5 

130 

20,000 

48 

14.1 

489 

50,000                                    70 

32.6 

2,825 

IOO,OOO 

120 

59.2 

10,250 

As  the  inductive  drop  upon  the  line  will  be  proportional  to 
the  working  current,  this,  as  may  be  seen  from  Table  V.,  is 
in  the  case  of  long  transmission  lines  strictly  limited,  and  will 
not  generally  exceed  100  amperes. 

A  further  consideration  limiting  the  working  current  is  that 
of  power  surges  or  rises  in  pressure  which  occur  when  the  line 
is  broken  or  short  circuited.  The  abnormal  pressure  rises 
encountered  under  such  conditions  are  found  to  depend  entirely 
upon  the  value  of  the  current.  It  thus  happens  that  a  line 
working  at  30,000  volts  with  a  load  current  of  100  amperes  may 
experience  greater  surge  pressures  than  a  line  working  at  60,000 
volts  with  a  load  current  of  50  amperes. 

Maximum  Economy. — The  direct  application  of  Kelvin's 
law  to  the  transmission  line  gives  the  conditions  under  which 
the  cost  of  transmitting  a  given  amount  of  power  along  the  line 
is  a  minimum.  It  does  not,  however,  take  into  consideration 
the  cost  of  insulating  the  line  for  extra  high  pressures,  and  this 


Three-Phase  Transmission 


becomes  of  much  greater  importance  in  the  case  of  underground 
cables. 

The  usual  condition  applied  to  an  overground  transmission 
line  is  : — 


Total  cost  of  transmitting  power 
Revenue  earned 


•  a.  minimum. 


.f" 


FIG.  2. 


In  this  case  the  charges  for  interest  and  depreciation  on  the 
total  cost  of  the  line  will  be  equal  to  the  cost  of  the  C2R  losses 
for  maximum  economy. 

Under  some  conditions  the  drop  in  pressure  along  the  line 
would  be  too  great  to  enable  regulation  for  constant  pressure  at 
the  receiving  end  to  be  efficiently  carried  out  if  the  most 
economical  section  of  conductor  were  employed  as  given  by 


Technical  Considerations  15 

Kelvin's  law.  Under  other  conditions  also  the  application  of 
the  law  may  be  precluded  by  the  excessive  heating  of  the 
conductors. 

Induction  boosters  placed  at  the  distributing  ends  of  trans- 
mission lines  for  compensating  the  line  drop  are  adopted  in 
some  cases.  This  apparatus  is,  however,  large  and  expensive, 
and  it  would  appear  that  the  more  general  practice  with  trans- 
mission schemes  now  is  to  vary  the  generator  voltage  with  the 
load,  keeping  the  line  drop  within  the  economical  range  of  voltage 
regulation  of  the  generator. 

It  is  usual  to  keep  the  copper  drop  on  the  line  down  to 


FIG.  3. 

about  10  per  cent.,  the  total  reactive  drop  at  full  load  being 
about  15  per  cent.  This  allows  of  regulation  for  approximately 
constant  pressure  at  the  receiving  end  of  the  line  by  the  adjust- 
ment of  the  generator  voltage. 

The  generators  are  mostly  separately  excited  by  inde- 
pendently driven  exciters,  and  have  a  range  of  regulation  in  their 
voltage  of  as  much  as  25  per  cent,  in  some  cases. 

It  is  interesting  to  note  that  the  application  of  Kelvin's  law 
in  a  modified  form  to  many  of  the  high-pressure  transmission 
lines  found  abroad  indicates  that  the  very  high  working  pressures 
adopted  are  in  keeping  with  the  conditions  of  maximum  economy. 

The   conductors    used  for  overground  transmission   are,   in 


1 6  Three-Phase  Transmission 

general,  constructed  of  cable  consisting  of  seven  or  nineteen 
strands,  which  have  greater  flexibility  than  solid  drawn  con- 
ductors. The  metals  used  in  the  construction  of  the  line  are 
either  of  copper  or  aluminium,  steel  being  used,  however,  in  very 
long  spans.  The  relative  advantages  of  copper  and  aluminium 
for  this  purpose  may  be  briefly  stated  as  follows  : — 

COPPER.  ALUMINIUM. 

Greater  mechanical  strength.  Lighter  than  copper  for  same  con- 
Easily  soldered  and  jointed.  ductivity. 
Corrosion     less     likely     than     with  Less  expensive. 

aluminium. 

Smaller    coefficient     of     expansion  Less  danger  of  "  corona "  effect  and 

than  aluminium,  and,  therefore,  loss   from   atmospheric    disper- 

less  sag.  sion. 

Less    cross    section    for    the    same  Less    rise   in    temperature    for    the 

resistance  than  aluminium,  and,  same    resistance    and    working 

therefore,    not   affected   to    the  current  than  with  copper. 

same  extent  by  wind  pressure. 

Although  aluminium  has  been  extensively  employed  for 
overhead  transmission  lines,  some  of  the  later  schemes  are 
adopting  stranded  copper  conductors. 

Protection  from  Lightning. — The  protection  of  the  overhead 
transmission  line  from  lightning  discharges  is  of  the  greatest 
importance,  although  engineers  in  charge  of  high-pressure  lines 
seem  somewhat  dubious  as  to  the  efficacy  of  most  forms  of 
lightning  arrester.  The  lightning  arresters  in  most  general  use 
are  of  electrolytic  type  arranged  with  a  spark  gap  between  them 
and  the  line. 

As  a  further  safeguard  against  lightning,  an  earthed  wire  is 
run  the  whole  length  of  the  line  supported  at  the  top  of  the 
transmission  towers  and  situated  about  6  ft.  above  the  line 
conductors.  Spark  gap  arresters  are,  in  this  case,  generally  also 
connected  to  the  line. 

The  general  experience  is  that  transmission  lines  insulated 
for  such  high  pressures  as  100,000  volts  appear  to  be  much  less 
affected  by  lightning  than  lines  used  at  lower  voltages. 


CHAPTER    II 
TRANSMISSION    LOSSES 

AN  account  of  the  losses  entailed  by  the  transmission  of 
electrical  energy  with  underground  cables  of  three-phase  type, 
paper-insulated,  lead-covered,  and  laid  in  cast-iron  troughs  or 
armoured  with  steel,  must  include  the  consideration  of  the 
following  :  — 

a.  Copper,    or   C2R,    loss    due   to   the   ohmic   resistance   R 
of  the  cores  of  the  cable  and  the  square  of  the  load  current  C 
at  every  instant. 

b.  Dielectric    hysteresis,    or    the    loss    due    to    mechanical 
stresses  in,  and  the  heating  of,  the  insulation  ;   the  specific  in- 
ductive   capacity   of    the    insulation    also    allows   a   condenser 
current  to  pass  and  gives  rise  to  a  further  C2R  loss  in  the  cores 
of  the  cable. 

c.  Sheath    loss   due  to  currents  induced  in  the  lead  sheath 
of  the  cable  by  the  varying  magnetic   field    produced    by   the 
alternating  currents  in  the  three  cores  of  the  cable. 

d.  Iron  loss  due  to  hysteresis  proper,  and  eddy  current  loss 
due  to  the  magnetisation  of  the  steel  armouring  or  cast-iron 
trough  enclosing  the  cable. 

With  regard  to  the  above  it  is  first  to  be  noted  that  losses 
a,  c,  and  d  depend  upon  the  square  of  the  load  current, 
whereas  loss  b  is.  independent  of  this  load  current,  except  in 
so  far  as  it  may  increase  the  temperature  of  the  cable  and 
diminish  the  resistance  of  the  dielectric. 

Copper  Losses.  —  As  regards  a,  with  a  varying  load  curve 
such  that  clt  c^  &c.,  represent  values  of  the  load  current  during 
intervals  tv  /2,  &c.,  and  R  represents  the  resistance  in  ohms 
of  one  core  of  the  cable,  the  total  loss  in  units  (with  a  three- 
core  cable)  in  any  given  period  is 

'8%  &c.) 


1,000 
'7 


1  8  Three-Phase  Transmission 

where  tv  /2,  &c.,  indicate  the  intervals  during  which  the  load 
current  had  the  corresponding  values  c^  c.2,  &c. 

If  we  denote  by  Cm  the  average  effective  current  and  by  T 
the  total  period  considered,  we  have  :  — 


0/ 


=     Ai2/i 

V 


That  is,  for  any  given  load  curve,  the  losses  during  the  interval 
T  would  be  the  same  as  if  the  current  had  remained  of  constant 
value  Cm,  which  is  obviously  the  square  root  of  the  mean  square 
of  the  current  varying  according  to  the  load  curve  considered. 

Dielectric  Losses.  —  With  regard  to  dielectric  loss  b  it  may 
perhaps  be  as  well  to  consider  briefly  at  this  point  the  physical 
phenomena  associated  with  insulating  media  subject  to  electrical 
pressure. 

A  .05  sq.  in.  three-core  20,000  volt  cable,  paper-insulated, 
has,  when  well  constructed,  an  insulation  resistance  of  about 
1,000  megohms  per  mile  at  a  temperature  of  70°  Fahr.  This 
means,  of  course,  a  certain  amount  of  leakage  current,  but 
as  the  loss  per  mile  from  this  cause  or  the  C2R  loss  in  the 
dielectric  only  amounts  to  1.2  watts  it  is  entirely  negligible,  upon 
the  assumption  of  constant  insulation  resistance  under  electrical 
stress. 

The  capacity  current  of  the  same  20,000  volt  cable,  assuming 
a  sine  pressure  wave  free  from  harmonics  at  50  cycles,  would  be 
approximately  0.74  ampere  per  mile,  although  in  practice  it  might 
be  much  greater  due  to  harmonics.  The  copper  loss  due  to  this 
current  is  given  by  C2R  (C  being  the  charging  current,  and  R 
the  resistance  of  one  core  of  the  cable),  and  is  only  0.4  watts 
per  mile,  and,  therefore,  for  short  cables  also  negligible.  It 
might  appear,  therefore,  that  the  really  important  loss  must  be 
looked  for  elsewhere,  and  was  to  be  found  in  the  so-called 
dielectric  hysteresis  loss  of  the  cable.  It  will  be  shown,  however, 
in  what  follows  that  the  open  circuit  copper  loss  under  certain 
conditions  with  long  cables  may  considerably  exceed  the  so- 
called  dielectric  loss. 

When  a  tube  of  insulating  material  is  subjected  to  a  difference 
of  electrical  pressure  between  its  inner  and  outer  face,  the  material 
is  electrostatically  strained  with  a  molecular  displacement  which 


Dielectric  Losses  19 

may  finally  end  in  the  complete  rupture  of  the  material  if  the 
difference  in  pressure  prove  sufficient.  If  the  pressure  be 
removed,  the  molecular  displacement  would  appear  in  most  cases 
to  gradually  recover  its  normal  unstrained  condition,  accompanied 
by  an  electrostatic  phenomenon  generally  known  as  a  soaking 
out  of  the  charge.  Whatever  may  be  the  real  mechanism  of 
this  phenomenon  the  result  remains  that  with  rapidly  alternating 
pressures  molecular  vibrations  are  set  up  in  the  dielectric,  heating 
it  and  causing  a  loss  of  energy  in  a  similar  manner  to  that  in 
which  the  rapid  alternate  magnetisation  and  demagnetisation  of 
a  piece  of  iron  causes  energy  to  be  frittered  away  in  the  form 
of  heat. 

Associated  with  this  loss  due  to  molecular  vibration  in  the 
dielectric  is  another  effect,  that  is,  the  decrease  in  resistance  of 
the  dielectric  as  the  time  of  its  electrification  is  made  shorter 
and  shorter.  This  is  well  seen  by  the  decrease  in  the  deflection 
of  a  mirror  galvanometer  used  to  measure  insulation  resistance 
by  the  direct  deflection  method  as  the  time  of  electrification  or 
period  of  the  test  is  extended,  usually  to  an  interval  of  one 
minute.  Now  with  a  cable  subjected  to  an  alternating  E.M.F. 
it  is  obviously  charged  during  one-quarter  of  a  period,  and  hence 
the  period  of  electrification  is  only  one-fourth  of  the  periodic 
time,  and  thus  exceedingly  short,  z>.,  between  T^o  second  and  ^^ 
second,  with  frequencies  of  25  and  100  periods  per  second 
respectively.  It  would,  therefore,  appear  that  the  resistance  of 
a  dielectric  to  an  alternating  pressure  may  be  many  times  less 
than  would  be  deduced  from  ordinary  measurements  of  insula- 
tion resistance,  and  consequently  the  loss  due  to  the  dielectric 
acting  as  a  conductor  may  be  proportionately  increased. 

The  charging  current  flowing  into  a  cable  due  to  capacity 
alone  would  have  a  phase  difference  of  90°  in  advance  of  the 
pressure,  and  would,  therefore,  be  wattless.  Owing  to  the  copper 
resistance,  however,  of  the  conductors  this  phase  difference  is  not 
exactly  90°,  since  the  copper  loss  has  to  be  supplied  by  means  of 
a  small  power  factor.  Finally,  the  losses  due  to  hysteresis  and 
conduction  in  the  dielectric  must  also  be  supplied  by  the  charg- 
ing current  and  pressure,  and  these  losses,  accordingly,  increase 
the  power  factor  of  the  cable  to  the  necessary  extent  by  bringing 
the  pressure  and  charging  current  more  nearly  into  phase. 

It  may  be  shown  that,  for  the  purpose  of  calculating  the 
charging  current  which  will  flow  into  a  three-phase  cable  with 


20  Three-Phase  Transmission 

symmetrical  cores  when  subject  to  an  applied  pressure  of  sine 
wave  form,  we  can  assume  that  the  three  conductors  themselves 
possess  no  capacity,  but  that  they  are  each  connected  to  the  lead 
sheath  of  the  cable  by  a  condenser  having  an  effective  capacity 
which  we  may  denote  by  K. 

If  we  measure  the  capacity  in  microfarads  between  one  core 
and  the  other  two  cores  connected  to  the  lead  sheath  and  call 
this  value  Kx ;  also  measure  the  capacity  between  all  three  cores 
bunched  together  and  the  lead  sheath  and  call  this  value  K9, 
then  the  value  of  the  effective  condenser  capacity  we  have 
denoted  by  K  is  given  in  microfarads  by  the  following  expres- 
sion : — 

K-x.5Kt-.x66K,. 

It  is  well  known  that  with  a  sine  wave  of  effective  pressure 
V  volts  and  frequency  n  complete  periods  per  second  applied  to 
the  terminals  of  a  condenser  of  capacity  K  microfarads,  the 
charging  current  C  in  amperes  is  given  by  the  expression  : — 

r  _  2JrV«K. 

I0« 

We  are,  therefore,  in  a  position  to  calculate  the  charging  current 
of  our  three-phase  cable. 

Let  us  take  as  a  practical  example  a  modern  three-phase  .05 
sq.  in.  paper-insulated  lead-covered  cable  constructed  for  a 
working  pressure  of  20,000  volts  between  conductors,  10  miles  in 
length,  connected  to  a  star- wound  generator  with  earthed  neutral 
point  and  developing  a  pure  sine  pressure  wave. 

Capacity  measurements  gave  the  following  results  : — 

One  core  versiis  two  other  cores  connected  to  lead  sheath,  i.e.,  Kx  - 

1.7  microfarads. 
All  three  cores  bunched  versus  lead  sheath,  i.e.,  K0  =  3  microfarads. 

Our  effective  condenser  capacity,  i.e.,  K,  is,  therefore, 
K  •=  1.5  x  1.7  -  .166  x  3  =  2.06  microfarads. 

Now  the  effective  pressure  charging  this  condenser  is --_— 

V3 
or  1 1,500  volts  above  earth  potential. 

Hence  our  charging  current  per  conductor  C  is  given  by : — 

^     27r  x  n, coo  x  150  x  2.06 

C  =  -  3          —  =  7.45  amperes. 


Cable  Power  Factor  21 

It  may  be  mentioned  here  that  a  .05  sq.  in.  three-core 
20,000  volt  paper-insulated  cable  with  a  dielectric  of  |  inch 
between  cores  and  lead  sheath,  when  pressure-tested  at  40,000 
volts  and  frequency  of  84  cycles  for  four  hours  between  one  core 
and  two  others  connected  to  lead  sheath,  was  found  to  have 
increased  in  temperature  by  36°  Fahr.  Similarly  with  a  pressure 
of  30,000  volts  the  temperature  rose  16°  Fahr.  in  nine  and  a  half 
hours.  This  temperature  rise  is  nearly  altogether  attributable  to 
dielectric  loss,  since  the  length  of  cable  tested  was  a  short  one, 
and,  therefore,  the  copper  loss  small.  Wattmeter  measurements 
showed  the  power  factor  of  this  cable  to  be  about  .028  with  the 
wave  form  used  in  the  test,  and  it  would,  therefore,  appear  that 
the  dielectric  loss  with  this  cable  in  practice  would  be  about 
.7  kw.  per  mile.  As  will  be  shown  later,  however,  the  power 
factor  of  any  cable  and  the  charging  current  will  be  largely 
influenced  by  the  presence  of  harmonics  in  the  wave  form  of  the 
applied  pressure. 

Probably  the  earliest  attempts  to  measure  dielectric  losses  on 
practical  cables  were  those  made  upon  the  Deptford  10,000  volt 
Ferranti  mains  by  Mr  D'Alton,  when  Chief  Engineer  to  the 
City  of  London  Company.  The  method  of  experiment  consisted 
in  carefully  indicating  an  engine  driving  an  alternator  between 
such  times  as  one  cable  after  another  was  switched  on  or  off. 
These  measurements  seemed  to  have  corresponded  with  a  power 
factor  of  .02  or  a  total  loss  of  about  I  kw.  per  mile  of  cable. 
Various  other  methods  have  been  adopted  by  other  experi- 
menters. Some  of  these  results  have  been  collected  for  refer- 
ence in  Table  VII. 

From  these  experimental  results  it  is  evident  that  we  shall 
in  general  be  fairly  safe  in  assuming  the  power  factor  of  a 
well-constructed  paper  cable  to  be  about  .028.  The  energy  loss 
in  watts  W  going  on  in  the  dielectric  of  a  three-phase  cable 
into  which  a  charging  current  of  C  amperes  is  flowing  under  the 
effect  of  an  applied  pressure  between  conductors  of  V  volts  is, 
accordingly,  given  by  : — 

W  =  C.V.  v/3x.o28. 

If  the  cable  is  a  very  long  one,  the  C2R  loss  due  to  the 
charging  current  C  flowing  through  the  conductors  of  the  cable 
of  resistance  R  will  become  of  importance,  and  may  considerably 
exceed  the  dielectric  loss. 


22 


Three-Phase  Transmission 

TABLE  VII. 


Authority. 

Type  of  Cable 
Working  Pressure  and 
Frequency. 

Power  Factor 
Observed. 

Method  of  Measure- 
ment. 

D'Alton      - 

Deptford        Mains 

.02 

Indicating  engines 

Ferranti        C.C. 

while  cables  were 

paper  -  insulated 

switched  on  and 

cables,        1  0,000 

off. 

volts,  87  ~ 

Sparks 

V.I.R.  C.C.  cable, 

•034 

D.C.  motor-driven 

2,000  volts,  ioo~ 

alternator. 

Mather 

V.I.R.    C.C.   cable 

•034 

Wattmeter  method. 

2,000  volts,  ioo~ 

Cable  alone,  and 

in    parallel,   and 

series  with  iron- 

less  choker. 

Ayrton  and 

British      Insulated 

.024-.028 

Wattmeter  method. 

Mather 

and  Helsby  C.C. 

Ironless    choker 

paper     cable, 

in    parallel    and 

2,000  volts,  loo  ~ 

series  with  cable. 

Do.    -        - 

Silvertown    V.I.R. 

.028 

Do. 

C.C.  cable,  2,000 

volts,  loo  ~ 

Mordey  and 

V.I.R.   C.C.  cable, 

.124 

Thomson     record- 

Minshall 

2,000  volts,  ioo  ~ 

ing  wattmeter. 

Do.    - 

V.B.     C.C.     cable, 

.124 

Motor-driven  alter- 

2,000 VOltS,  IOO  ~ 

nator.       Swin- 

burne wattmeter. 

Hoor 

Paper  cable,  2,000 

.025 

Wattmeter. 

volts,  50  ~ 

British  Insulated 

Helsby     rubber 

.O228-.O255 

Wattmeter     and 

and      Helsby 

cables,  C.C.  50  ~ 

choker     as     in 

Cables  Ltd. 

and  ioo  ~,  2,000 

Ayrton's    experi- 

volts. 

ments. 

Do.   - 

Three-core  .05   sq. 
in.     20,000    volt 

.028 

Do. 

paper  cable 

To  arrive  at  the  value  of  this  copper  loss  due  to  the  charging 
current  we  must  bear  in  mind  that  this  current  continuously 
diminishes  in  value  as  it  travels  along  the  cable  from  the  sending 
end.  In  the  case  of  any  one  core  of  a  cable  of  resistance  R  ohms 
into  which  a  charging  current  of  C  amperes  is  flowing  at  the 
sending  end,  it  is  readily  shown  that  the  total  copper  loss  W  in 
watts  is  given  by  : — 


Lead  Sheath  Losses  23 

or  the  equivalent  current  C1  which  would  produce  the  same  loss 
if  uniformly  distributed  along  the  cable  is 


Taking  all  three  cores  of  our  three-phase  cable  into  con- 
sideration, we  get  the  total  copper  loss,  C2R. 

Lead  Sheath  Losses.  —  The  sheath  losses  in  the  case  of  a 
three-core  cable  will  depend  upon  — 

1.  The  distribution  and  variation  in  the  magnetic  field  set  up 
by  the  currents  in  the  cable  cores  in  air  or  other  non-magnetic 
medium. 

2.  The  extent  to  which 
this  field  is  augmented  by 
the    cast  -  iron    trough    or 
steel   armouring  by  which 
the  cable  is  enveloped. 

3.  The  ohmic  resistance 
of  the  lead  sheath  to  the 
currents  induced  in   it  by 
the  E.M.F.  produced  by  the 
varying  magnetic  field. 

It  has  also  been  fairly 
well  established  experi- 
mentally that  the  following 

laws  hold  with   regard   to  FlG    ~ 

sheath  loss  :  — 

1.  It  is  directly  proportional  to  the  length  of  the  cable. 

2.  It  increases  as  the  square  of  the  current  in  the  cores. 

3.  It    is   very   nearly   proportional    to    the    square    of    the 
frequency. 

4.  It  is  inversely  proportional  to  the  resistance  of  the  lead 
sheath,  and  hence  approximately  proportional  to  its  thickness 
with  a  given  diameter  over  dielectric. 

If  we  imagine  the  lead  sheath  divided  into  three  segments, 
each  situated  symmetrically  over  one  core  of  the  cable,  Fig.  4, 
the  total  current  in  each  segment  will  be  in  quadrature  with  the 
current  in  the  core  adjacent  to  it,  and  its  value  may  be  approxi- 
mately arrived  at  by  calculation  from  the  known  relation  between 
two  mutually  inductive  circuits  in  air  :  — 


Three-Phase  Transmission 


To  get  a  rough  idea  of  the  manner  in  which  the  E.M.F.'s 
are  induced  in  the  lead  sheath  we  will  assume  that  the  current 
in  each  conductor  rises  to  a  maximum,  decreases  and  passes 
through  zero  to  a  negative  maximum  in  accordance  with  a  sine 
law.  If  at  time  o  we  suppose  the  current  in  core  No.  I,  Cp  to  be 
100  amperes,  the  successive  values  of  the  currents  C1,  C2,  C3  at 
equal  time  intervals  of  30°  will  be  as  shown  by  the  following 
table  :— 

TABLE  VIII. 


Time. 

CP 

C2. 

C3. 

o 

100 

5° 

50 

30 

86 

o 

86 

60 

50 

5° 

IOO 

90 

o 

86 

86 

120 

50 

IOO 

50 

150 

86 

86 

0 

1  80 

100 

5° 

5° 

If  we  imagine  the  currents  induced  in  the  three  segments 
of  the  sheath  to  have  equal  values  to  those  in  the  three  cor- 
responding cores,  their  relative  values  are  given  by  the  first  and 
fourth,  second  and  fifth,  &c.,  lines  in  the  above  table. 

Now  it  is  evident  that  although,  owing  to  the  symmetrical 
arrangement  of  the  three  cores  of  the  cable,  the  variation  in  the 
distribution  and  strength  of  the  field  throughout  a  complete 
cycle  may  be  calculated  and  plotted  in  a  diagram,  provided  no 
magnetic  material  such  as  an  iron  envelope  is  in  the  neighbour- 
hood of  the  cable ;  yet  it  is  difficult  to  predict  to  what  extent 
the  field  produced  by  the  cable  cores  is  augmented  by  iron 
envelopes  such  as  cast-iron  troughing  or  steel  armour,  and, 
further,  in  what  manner  the  natural  distribution  of  the  field  is 
interfered  with. 

In  order  to  test  this  point  the  writer  prepared  a  search  coil 
of  rectangular  form  22  cm.  in  length  and  I  cm.  in  width,  and 
composed  of  124  turns  of  fine  wire.  The  search  coil  was  suffi- 
ciently narrow  to  allow  of  its  being  inserted  in  any  position 
round  the  periphery  of  the  cable,  illustrated  by  Fig.  4  (the 
usual  jute  layer  between  armour  and  lead  having  been  removed), 
or  in  a  similar  manner  between  the  lead  sheath  and  the  cast- 


Lead  Sheath  Losses 


iron  troughing  enclosing  the  cable.  Direct  currents  were  then 
passed  through  the  three  cores  of  the  cable  corresponding  in 
value  and  sign  to  those  at  different  instants  throughout  a 
complete  period  when  working  three-phase. 

The  search  coil  having  been  previously  connected  to  a 
carefully  standardised  Ayrton  &  Mather  Ballistic  Galvanometer 
the  throw  of  the  needle  when  the  direct  current  circuits  through 
the  cores  were  interrupted  was  carefully  noted. 

The  following  readings  (Table  IX.)  illustrate  the  results 
obtained  : — 

TABLE  IX. 


Position  of  Search 

.=  •3 

Position  of  Search 

Coil  and  Number 

Coil  and  Strength 

of  Times  Field  is 

SJ  v    - 

DIAGRAM. 

Particulars  of 
Cable. 

of  Field  in  C.G.S. 

Greater  than  with 
Cable  Unenclosed 

!!<- 

|i 

A 

B 

c 

A 

B 

c 

A 

Unenclosed 

I  73 

2  ^8 

I  70 

(©©) 

In  C.I.  trough  - 

3-°4 

4-61 

2.38 

-.75 

1.92 

i-33 

1.66 

v^ 

Steel  armour    - 

2.28 

3-72 

2-53 

1.32 

i-55 

1.41 

1.42 

A 

I  IQ 

I  q8 

2  71 

y"g)\ 

(  (S)  (^)  ) 

In  C.I.  trough  - 

2.5 

.228 

4.6 

2.08 

1.1111.7 

1.63 

v^ 

Steel  armour    - 

1.68 

•34 

3-73 

1.41 

1.69  |  1.38 

1 

1.47 

It  might  appear  at  first  sight  that  the  above  values  obtained 
for  strength  of  field  under  various  conditions  are  much  smaller 
than  would  be  expected  from  the  large  currents  traversing  the 
cores  of  the  cable.  The  explanation  is,  however,  not  far  to  seek, 
and  the  discrepancy  is  due  to  the  fact  that  as  the  plane  of  the 
coil  was  necessarily  tangential  to  the  circumference  of  the  cable 
the  direction  of  the  lines  of  force  was  in  no  case  normal  to  the 
plane  of  the  test  coil.  Nevertheless  a  comparison  of  such 
readings,  taken  with  as  nearly  as  possible  identical  positions  of 


26  Three-Phase  Transmission 

the  search  coil  and  the  same  current  values  first  without  and 
then  with  the  iron  envelope  surrounding  the  cable,  should  still 
represent  with  close  approximation  the  extent  by  which  the 
external  field  of  the  cable  is  augmented  by  the  troughing  or 
armouring. 

Coming  now  to  the  direct  measurement  of  lead  sheath  losses 
upon  underground  cables,  this  is  in  practice  usually  accompanied 
by  some  difficulty  arising  from  the  following  amongst  other 
points. 

(1)  The  loss  to  be  measured  is  generally  such  a  small  fraction 
of  the  total  load  carried  by  the  cable  at  high  pressure  that  direct 
measurement  by  the  ordinary  switchboard  wattmeters  is  out  of 
the  question. 

(2)  Measurement  by  currents  at  low  potential  are  likely  to 
be  seriously  affected  by  variation  in  the  copper  resistance  of  the 
cable  from  rise  in  temperature  during  the  test,  on  account  of  the 
large  currents  usually  necessary  to  reproduce  working  conditions 
of  field,  &c. 

If  the  three  cores  of  an  underground  high-pressure  cable  be 
joined  together  at  the  far  end  and  three-phase  current  at  low 
pressure  be  passed  through  the  cable,  from  observations  of  the 
potential  difference  V  in  volts  between  the  cores  of  the  cable 
and  the  current  C  in  amperes  flowing  into  each  core  at  the 
sending  end,  the  impedance  per  core  in  ohms  is  given  by 


If  we  measure  also  the  copper  resistance  per  core  R  in  ohms 
the  product  CR  gives  us  the  effective  E.M.F.  (e\ 

Owing  to  the  fact,  however,  that  the  lead  sheath  of  the  cable 
is  acting  as  a  closed  secondary  circuit  to  each  core  of  the  cable  as 
a  primary  circuit,  the  power  factor  cos  <t>  will  not  be  given  by  the 

quotient  e.^,  since  the  effect  of  the  closed  secondary  will  be  to 

y 
bring  the  impressed  pressure  — =  and  the  effective  pressure  (e) 

? 

more  nearly  into  phase  than  is  indicated  by  the  value  of  <£  so 

obtained.  Oscillograph  records  of  P.D.  and  current  in  the  case 
of  a  cable  of  the  size  shown  in  Fig.  4  showed  that  <j>  was  small, 
and  hence  cos  <$>  was  practically  unity. 


Lead  Sheath  Losses  27 

There  is  no  doubt,  however,  that  the  lead  sheath  losses  will 
lie  between  the  values 

/  V        \  /  V  \ 

C(—7=-e}  and  C(— 7=  cos  <f>-e), 

\  V3      /  V  -s/3  / 

or  the  apparent  watts  less  copper  watts  with  assumed  angles  of 
lag  zero  and  <i>  respectively. 

It  may,  therefore,  be  of  interest  to  ascertain  the  maximum 
values  such  losses  could  reach  in  practice. 

In  Table  X.  are  set  out  observations  made  upon  a  length  of 
5,480  yds.,  i.e.,  3.11  miles,  of  this,  0.15  sq.  in.  three-core  6,000 
volt  cable,  having  a  lead  sheath  0.25  in.  in  thickness,  and  enclosed 
in  a  cast-iron  trough  4^  in.  by  4^  in.  by  f  in.  in  thickness,  the 
full-size  section  of  the  cable  being  given  by  Fig.  4. 

The  resistance  of  each  core  was  found  to  be  0.901  ohm. 


TABLE  X. 


Amps. 

V 

VI 

vc 

V5 

C2R 

i- 

24.5 

25 

612 

54i 

71 

30.8 

3o-5 

940 

853 

87 

35-4 

35-2 

1,246 

1,127 

119 

34-i 

34-3 

1,175 

1,048 

122 

31-25 

31-25 

975 

880 

95 

25.5 

25.6 

652 

587 

65 

From  the  above  table,  allowing  for  ordinary  errors  of  observa- 
tion in  the  readings  of  ammeters  and  voltmeters,  it  will  be  seen 
that  the  maximum  loss  as  represented  by  the  last  column  in- 
creases closely  as  the  square  of  the  current  in  the  cable  cores. 
Assuming  the  full  load  current  of  this  cable  to  be  1 30  amperes  per 
core,  the  maximum  loss  per  mile  with  all  three  cores  would  be 

(  )    x x  •?,  say  =  i ,  7 1  o  watts. 

\34-i/       3-11 

Now  it  was  found  that  the  effect  of  the  cast-iron  trough  was 
to  increase  the  strength  of  field  surrounding  the  cable  by 
1.64  times,  whereas  steel  armouring  increased  the  strength  of 
field  by  1.44  times  its  value  in  air. 

As    the   sheath   losses   will    vary   as   the   squares   of  these 


28  Three-Phase  Transmission 

numbers  we  arrive  finally  at  the  following  maximum  values  of 
the  lead  sheath  losses  in  the  cable  considered. 


TABLE  XI.— Loss  IN  KVV.  PER  MILE  AT  130  AMPERES 
PER  THREE  CORES  AT  50  ~. 


Cable  enclosed  by 
C.I.  Trough. 

Cable  enclosed  by 
Steel  Armour. 

Cable  unenclosed 
in  Air. 

I.7I 

1.320 

.636 

Board  of  Trade  Regulations. 

Having  briefly  reviewed  the  nature  and  order  of  the  losses  to 
be  met  with  in  underground  E.H.P.  three-phase  mains,  it  is  of 
interest  to  consider  at  this  stage  the  influence  of  the  Board 
of  Trade  Regulations  upon  transmission  schemes  employing 
these  cables. 

Regulation  B,  Clause  2,  of  the  E.H.P.  Regulations  of  the 
Board  of  Trade,  dated  1906,  reads  as  follows  : — 

"A  main  for  an  extra  high-pressure  supply  shall  not,  without  the  consent 
in  writing  of  the  Board  of  Trade,  be  used  for  the  transmission  of  more  than 
1,000  kilowatts  unless  adequate  provision  is  made  for  an  emergency  supply 
in  the  event  of  the  breakdown  of  the  main." 

Although  the  Board  of  Trade  will,  in  accordance  with  their 
usual  practice,  consider  each  case  upon  its  merits,  and  in  general 
issue  their  consent  in  cases  where  the  commercial  aspect  of  the 
question  would  otherwise  irretrievably  hinder  electrical  progress, 
yet  the  result  of  the  1,000  kw.  limit  per  cable  if  rigidly 
enforced  would  prove  somewhat  hard  upon  some  electrical 
undertakings,  as  will  be  shown  in  what  follows. 

The  first  point  which  will  be  at  once  apparent  is  that  a 
number  of  similar  cables  in  parallel  will  be  required  according  to 
the  load  to  be  transmitted  to  each  point,  and  since  on  the 
grounds  of  safety  the  Board  of  Trade  recommend  that  trunk 
feeders  should,  if  possible,  take  different  routes,  the  cost  of 
trenchwork  will  in  general  be  in  proportion  to  the  number  of 
cables  required.  In  addition  extra  expense  is  involved  in  the 
cost  of  cable.  For  instance,  with  a  20,000  volt  transmission,  two 
.025  three-core  cables  laid  and  jointed  would  cost  ^2,528  per 


Pressure  Regulation  29 

mile  as  compared  with  £1,544  per  mile  for  a  three-core  .05  cable 
under  similar  conditions. 

The  second  point  to  be  considered  is  the  effect  upon  the 
working  losses  if  each  cable  be  laid  for  transmitting  1,000  kw. 

In  considering  this  point,  we  must  first  settle  the  means  to 
be  adopted  for  maintaining  approximately  constant  pressure  at 
the  receiving  ends  of  the  cables. 

For  the  purpose  of  distributing  electrical  energy  over  any 
extended  area,  one  or  several  generating  stations,  according  to 
the  nature  of  the  problem,  may  be  efficiently  employed.  There 
is,  however,  in  every  case  the  consideration  of  pressure  regulation 
at  the  generating  stations  or  in  the  substations  to  compensate 
for  the  drop  in  pressure  in  the  transmission  cables  or  the  line 
loss.  The  large  standard  types  of  alternators  used  at  the  present 
time  in  power  stations  are  not  suitable  for  giving  their  output  at 
widely  different  pressures.  Since  such  machines  are  required  to 
give  their  maximum  pressure  with  maximum  load  they  would  of 
necessity  have  to  be  run  much  under-excited  at  times  of  light 
load  when  the  line  drop  was  small,  by  means  of  main  field 
rheostats,  that  is,  if  the  range  of  pressure  variation  assumed  be 
greater  than  can  be  dealt  with  by  a  shunt  regulated  exciter. 
Under  such  conditions  the  regulation  of  pressure  would  be  very 
unstable,  the  voltage  creeping  up  or  down  after  every  adjustment 
of  the  rheostat,  and  every  fluctuation  in  the  load  would  be 
accompanied  by  wide  variation  in  pressure.  Quite  apart  from 
this,  there  is  always  present  the  necessity  of  keeping  some 
circuits,  if  only  local  lighting  circuits  and  those  dealing  with 
motor-driven  auxiliaries,  at  approximately  constant  pressure. 

The  question  of  boosting  the  whole  or  portion  of  the  output 
of  the  generating  station  must  in  every  case  be  considered  on  its 
merits,  and  the  working  costs  of  the  booster  with  the  particular 
load  curve  to  be  met  considered  side  by  side  with  the  interest 
charges  on  the  capital  cost  of  the  extra  copper,  which  if  put 
into  the  line  or  cable  system  would  render  boosting  unnecessary. 
The  writer  has  met  with  cases  where  the  double  transformation 
of  the  load  to  enable  boosting  to  be  effected  involved  an  annual 
cost  of  as  much  as  £i  per  kw.  transmitted  with  a  lighting  load 
curve. 

Where  the  station  output  is  transmitted  for  lighting  purposes, 
and  it  is  necessary  to  supply  various  trunk  mains  of  different 
length  in  which  the  peak  of  the  load  occurs  at  different  times, 


30  Three-Phase  Transmission 

the  adjustment  of  pressure  at  the  generating  station  bus  bars 
will  not  suffice  to  maintain  constant  pressure  at  the  various 
points  of  distribution.  If  the  trunk  cables  also  transmit  a  motor 
load,  it  is  not  possible  to  avoid  by  regulation  at  the  generating 
station  variations  in  the  pressure  at  the  distributing  points 
arising  from  the  fluctuations  in  the  load. 

By  the  use  of  booster  bus  bars  the  pressure  on  one  or 
more  groups  of  trunk  cables  of  approximately  equal  length 
may  be  adjusted  simultaneously  at  the  generating  station  or 
the  regulation  may  be  effected  at  the  substation  ends  of  each 
set  of  cables. 

A  common  form  of  booster  for  such  service  consists  of  two 
parts,  rotor  and  stator,  as  in  a  three-phase  induction  motor,  the 
windings  in  the  simplest  case  being  connected  in  series.  By 
means  of  a  worm  gear  and  hand-wheel  (or  automatically  if 
desired)  the  rotor  can  be  displaced  relatively  to  the  stator.  We 
have,  in  fact,  a  static  transformer  in  which  the  primary  and 
secondary  circuits  are  movable  relatively  to  one  another,  and, 
according  to  the  position  of  the  rotor,  relatively  to  the  stator ; 
the  resultant  pressure  of  the  rotor  or  one  of  its  components  will 
add  to  or  diminish  the  stator  pressure. 

Such  induction  boosters  have  the  advantage  of  possessing  a 
continuous  range  of  regulation,  and  also  allow  of  fine  adjustment 
throughout  their  range,  whereas  boosting  transformers  with  stops 
only  give  a  limited  number  of  fixed  pressures,  and  regulating 
switches  with  such  transformers  are  usually  limited  to  working 
voltages  of  between  2,000  or  3,000  volts. 

The  pressure  induced  by  the  rotor  windings  will  vary  from 
zero  to  a  maximum  value  positive  or  negative  according  to  its 
position  relatively  to  the  stator. 

Where  the  regulation  is  required  to  be  effected  on  an  E.H.T. 
circuit  the  rotor  winding  of  the  booster  is  usually  fed  by  a 
transformer,  permitting  of  the  movable  portion  of  the  booster 
working  at  low  pressure. 

Fig.  5  illustrates  the  usual  connections  in  such  cases. 

Some  financial  considerations  governing  the  application  of 
boosting  appliances  will  be  found  set  out  in  Chapter  VII. 

An  alternative  is  to  employ  separate  steam-driven  exciting 
plant  in  combination  with  shunt  or  main  field  regulation  to  give 
the  required  variation  in  the  pressure  of  the  generator. 

Another  method  of  regulation  consists  in  employing  syn- 


Pressure  Regulation  31 

chronous  motors  at  the  receiving  end  of  the  line,  and  by  varying 
the  excitation  of  the  synchronous  motors  compensating  for 
inductive  drop  in  the  line  and  low  power  factor. 

Each   of  the   above    boosting    arrangements,   however,   in- 
volves : — 


FIG.  5. 

(1)  Complication  of  switchgear  and  control. 

(2)  Increased  liability  to  breakdown. 

(3)  Extra  cost  in  capital  and  running  charges. 

In  general  with  such  E.H.P.  distribution  schemes  as  are  likely 
to  be  adopted  in  the  British  Isles,  the  range  of  regulation  obtain- 
able by  a  direct-driven  exciter  upon  the  alternator  shaft  will  be 


32  Three-Phase  Transmission 

found  convenient  and  economical,  any  extra  long  feeders  being 
regulated  by  boosters  either  at  the  generating  station  or  at  the 
substations.  We  may,  therefore,  discuss  at  some  length  this 
more  general  case. 

3000-K.W.    THREE-PHASE    ALTERNATOR. 


120 


CO 
U 
CO 
§  80 


I 

100 
90 

8c 


800  IGOO  24CO  3200 

KILOWATT    OUTPUT. 


A  =  Total  Excitation  Loss. 
B=xArmature  Copper  Loss. 
C  =  Commercial  Efficiency. 


D- Total  Electrical  Losses. 

E  =  lron  Wind  and  Friction  Losses. 

Fr^  Total  Losses. 


FIG.  6. 


With  three-phase  alternators  of  1,000  to  3,000  k\v.  output, 
the   excitation    required    by  the   main    field    will    generally  be 


Pressure  Regulation  33 

between  7  and  10  kw.  (see  Fig.  6)  involving  currents  of  200 
amperes  and  upwards  in  the  main  field,  if  the  common  practice  of 
a  low  voltage  exciter  be  followed  ;  with  such  machines  regulation 
by  rheostats  in  the  main  field  requires  the  use  of  large  resistances 
which  are  both  costly  in  themselves  and  wasteful  in  operation 
the  more  economical  method  being  the  insertion  of  a  regulating 
rheostat  in  the  shunt  winding  of  the  exciter.  This  method  of 
regulation  has,  however,  the  following  characteristics  : — 

(1)  At  light  loads  when  considerable  resistance  is  inserted  in 
the  shunt  winding  of  the  exciter,  regulation  becomes  somewhat 
unstable,  due  to  the  voltage  of  the  exciter  requiring  some  time  to 
attain  a  steady  value  after  operating  the  rheostat,  and  in  addition 
the  weak  field  of  the  alternator  is  likely  to  cause  considerable 
variations  in  terminal  pressure  with  even  small  fluctuations  in 
the  load. 

(2)  The  total  rise  in  the  pressure  of  the  alternator  at  full  load 
is  usually  limited  to  about  10  per  cent. 

As  it  will  be  as  well  to  keep  a  margin  of  not  less  than  5  per 
cent,  in  hand  of  the  possible  regulation  to  cope  with  irregularity 
in  steam  supply,  emergency  loads,  &c.,  and  an  allowance  of  at 
least  3  per  cent,  at  the  receiving  end  of  the  line  to  make  up  the 
voltage  drop  on  the  transformers  and  distribution  system  of 
mains,  it  will  be  seen  that  a  line  loss  of  2  per  cent,  or  thereabouts 
would  be  convenient  (if  we  exclude  boosting  apparatus)  with 
this  system  of  generating  and  transmitting  at  extra  high 
pressure.  No  account  has  been  taken  of  the  hand  regulation  of 
the  engine  governor  which  would  generally  be  available,  since 
the  resulting  variation  in  the  frequency  entailed  thereby  should 
be  discountenanced  in  ordinary  working. 

On  the  basis  of  a  2  per  cent,  line  loss  and  the  transmission  of 
1,000  kw.  per  cable,  the  following  table  gives  the  approximate 
sectional  area  and  cost,  laid  and  jointed,  of  three-phase  extra 
high-pressure  paper-insulated  lead-covered  cables  armoured  and 
suitable  for  delta  working  at  various  pressures  over  the  distances 
stated.  The  prices  of  the  cables  in  each  case  are  based  upon 
copper  electrolytic  wire  bars  at  .£120  per  ton  and  lead  at  £20 
per  ton,  the  highest  prices  which  have  held  in  recent  years.  It 
will  be  hardly  necessary  to  point  out  that  had  we  assumed  a 
different  percentage  line  loss  and  other  prices  for  copper  and 
lead  similar  features  would  have  been  exhibited  to  those  illus- 
trated by  the  table  under  consideration. 
3 


34 


Three-Phase  Transmission 


TABLE  XII. — APPROXIMATE  SECTIONAL  AREA  AND  COST 
OF  THREE-PHASE  TRUNK  MAINS  TRANSMITTING  1,000 
K.W.  WITH  A  LINE  Loss  OF  2  PER  CENT. 

The  Cables  are  insulated  for  Delta  working. 


5  Miles. 

10  Miles. 

15  Miles. 

20  Miles. 

50  Miles. 

Voltage 

of  Trans- 

mission. 

Area 

Cost 

Area  1     Cost 

Area 

Cost 

Area      Cost 

Area 

Cost 

per 
Core. 

per 

Mile. 

per 
Core. 

Mile. 

Core. 

per 
Mile. 

ofre.     Mile. 

Core. 

Mile. 

£ 

£ 

£ 

£ 

£ 

5.OOO 

40 

2  Q28 

) 

10,000 

.IO 

1,300 

.2 

2,034 

•3 

2,604 

•4         3,240 

15,000 

•05 

1,192 

.IO 

1,584 

•IS 

i,955 

.2         |  2,242 

.50 

4,105 

20,000 

.025 

1,264 

.05 

i,544 

.075 

1,760 

.10       1,956 

.250 

2,958 

25,000 

... 

•°35 

1,815 

.05 

1,946 

.075      2,220 

•175 

3,050 

30,000 

.025 

2,122 

•035 

2,245 

.05         2,414 

.125 

3,Ho 

As  might  be  expected,  for  each  distance  stated  a  minimum 
in  first  cost  is  obtainable  by  varying  the  pressure  of  transmission 
in  accordance  therewith.  It  is  interesting  to  note  that  a  trans- 
mission pressure  of  20,000  volts  would  appear  most  economical 
under  the  conditions  assumed  for  distances  between  10  and 
50  miles. 

In  addition  to  the  economies  to  be  effected  in  first  cost  under 
Board  of  Trade  Regulations,  it  is  only  right  to  consider  the 
possible  economies  to  be  effected  in  working  where  a  number 
of  cables  in  parallel  are  employed  to  transmit  a  given  load. 

We  have  already  seen  that  the  copper,  lead  sheath,  and 
armouring  or  iron  trough  losses  depend  upon  the  square  of  the 
load  current  whilst  the  loss  in  the  dielectric  is  practically  inde- 
pendent of  the  load  current,  unless  unduly  heated  thereby.  It 
is,  therefore,  obvious  that  for  any  number  n  of  similar  feeders 
in  parallel : — 

The  copper,  lead  sheath,  and   iron   losses    oc  -,  whilst  the 

dielectric  loss  oc  n. 

If  we  suppose  the  copper,  lead  sheath,  and    iron   loss  for 

T7- 

the  transmission  of  a  certain  number  of  kilowatts  = — ,  and  the 

n 

dielectric  loss  with  n  feeders  in  parallel  =  kn,  we  have  to  deter- 
mine the  conditions  under  which  the  total  loss  W  due  to  copper, 


Economies  in  Working 


35 


lead  sheath,  iron  and  dielectric  is  a  minimum,  that  is,  — \-kn 

n 

/K 

must  be  a  minimum.     This  is  obviously  the  case  when  ?/  =  »/__. 

v    k 

Take  the  case  of  6,000  kw.  transmitted  6  miles  at  10,000  volts. 
This  would  mean  at  least  six  cables  on  the  basis  of  1,000  kw. 
per  cable  without  taking  into  consideration  a  suitable  number 
of  spares,  which  would  in  most  cases  be  necessary. 

The  full  load  current  in  the  cores  of  each  cable  would  be 
about  60  amperes. 
Assume — 

(a)  Copper  loss  at  full  load,  2  per  cent.     =      20  kw. 
Sheath  loss,  i  kw.  per  mile  =        6    „ 

Iron  loss,  0.5  kw.  per  mile  =        3    „ 


(b)  Dielectric  loss,  2  kw.  per  mile 
The  most  economical  number  (#)  of  feeders  to  use  in  parallel 
under  the  above  conditions  is  given  by 

3.8  or  4  nearly. 

If  we  denote  by  C  the  total  load  current 
C2  x  J  =  29  x  6  =  1 74  kw. 
where  J  is  a  constant  and  all  six  cables  are  working  at  full  load. 

•     T=  X74><  io3 
'    J      (60x6)- 

=  1-34. 
ror  maximum  economy 

V    12  x io3 
.'.  n  — . 01055  C. 

We,  therefore,  should  vary  the  number  of  feeders  in  parallel 
according  to  the  load  for  maximum  economy  in  working,  as 
follows  : — 

TABLE  XIII. 


Amperes. 

Feeders. 

Amperes. 

Feeders. 

95 

, 

378 

4 

190 

2 

475 

5 

283 

3 

570 

6 

36  Three-Phase  Transmission 

To  summarise  the  preceding  considerations,  it  would  appear 
that  maximum  economy  would  be  effected  by  switching  off 
trunk  mains  at  times  of  light  load,  varying  the  number  in 
parallel  according  to  the  load  curve.  In  connection  with  this 
point  it  may  be  observed  that  the  oscillograph  has  conclusively 
proved  that  with  oil  switches  the  operation  of  switching  off  high- 
pressure  cables  is  perfectly  safe  since  the  current  is  always 
broken  when  passing  through  or  about  the  zero  value.  A  danger 
exists,  however,  in  switching  on  an  open  ended  cable  resulting 
in  the  formation  of  oscillations  of  double  pressure,  due  to  reflected 
waves  from  the  open  end.  This  difficulty,  great  as  it  may  seem, 
is  not  by  any  means  insurmountable.  One  safety  method  is  to 
connect  a  three-phase  transformer  to  the  open  end  of  the  cable 
before  making  it  live,  the  secondary  of  the  transformer  being 
closed  through  a  water  resistance,  subsequently  disconnecting 
the  transformer  when  the  cable  has  been  switched  on.  A  further 
method  is  to  arrange  the  switchboard  with  ring  bus  bars  at  the 
generating  station  divided  into  sections  consisting  of  feeder  and 
generator  panels  with  interconnecting  switches.  This  allows  of 
any  one  or  more  trunk  feeders  being  made  live  gradually,  and 
paralleled  with  other  live  feeders.  The  objection  to  this  method 
is  the  cost  of  starting  up  large  generators  solely  for  the  purpose 
of  making  cables  live.  A  third  method  is  to  employ  a  water 
resistance  charging  gear.  A  still  further  method  is  the  use  of 
a  motor  generator  to  make  the  cable  live  gradually  but  at 
constant  frequency.  With  a  well-constructed  paper-insulated 
cable,  however,  capable  of  withstanding  with  safety  a  temporary 
rise  in  pressure  of  three  or  more  times  the  working  pressure,  such 
devices  would  appear  to  be  unnecessary,  and  the  direct  switching 
on  of  such  cables  becomes  permissible. 

Kelvin's  Law. — Kelvin's  law  states  that  the  maximum  of 
economy  is  attained  in  transmitting  a  given  amount  of  power  at 
fixed  voltage  at  the  receiving  end  of  the  line,  when  the  annual 
cost  of  the  C2R  loss  in  the  line  is  equal  to  the  annual  interest 
and  depreciation  charges  on  that  part  of  the  line  the  cost  of 
which  varies  as  the  sectional  area  of  the  conductors. 

If  the  cost  of  one  conductor  of  the  line  in  £,  per  mile  is 
expressed  by  A  +  Btf,  a  being  its  area  in  square  inch  and  A  and 
B  constants,  e  equals  rate  per  cent,  for  interest  and  depreciation 
on  capital  _expenditure;  C  equals  average  effective  current  in 


Kelvin's  Law  37 

amperes  per  wire ;  K  equals  cost  of  generating  I  E.H.P.  per 
annum,  including  all  annual  charges,  then  it  may  be  shown  that 
the  most  economical  sectional  area  to  adopt  is  given  by : — 

/  jr 

a  =  .0755  CA/  — -   for  copper  conductors, 
and  the  most  economical  current  density — 

e—  for  copper  conductors. 

JV 

The  average  cost  of  i  E.H.P.  per  annum  of  8,760  hours  is 
approximately  £6.8,  with  a  number  of  hydro-electric  plants, 
although  this  varies  considerably  with  different  undertakings. 
This  figure  corresponds  to  a  total  cost  per  unit  generated  of 
0.25  penny. 

Interest  and  depreciation  on  the  capital  cost  of  the  conductors 
of  the  overhead  line  may  be  taken  at  1 5  per  cent. 

The  cost  of  the  conductors  will  vary  with  their  sectional  area 
and  the  cost  per  ton  of  the  metal  of  which  they  are  composed. 
With  stranded  copper  conductors,  we  may  assume  that  the 
weight  per  ton  per  mile  is  : — 9.36  x  a  approximately  ;  where 
a  is  the  total  sectional  area  in  square  inch. 

Thus  with  drawn  copper  at  £,6$  per  ton,  the  cost  of  I 
mile  of  conductor  of  sectional  area  a  square  inch  would  be 
£609  x  a. 

Under  the  above  conditions  we  get  for  our  sectional  area : — 


or  a  =  C  x  .00197. 

Thus  if  C  equals  100  amperes,  a  equals  .197  sq.  in.,  or  each 
conductor  would  have  a  sectional  area  of  approximately  .2 
sq.  in.  The  current  density  is  thus  500  amperes  per  square 
inch,  and  with  this  current  density  the  drop  in  volts  along  each 
conductor  would  be  about  22  volts  per  mile. 

It  is  to  be  specially  noted,  however,  that  the  above  calculation 
takes  no  account  of  the  cost  of  insulating  the  line,  and  a  more 
useful  condition  to  apply  is  that  the  cost  of  the  C2R  losses  shall 
be  equal  to  the  whole  of  the  charges  for  interest  and  depreciation 
on  the  transmission  line. 

The  cost  of  flexible  steel  supports  and  insulators  for  a  line 
insulated  for  60,000-80,000  volts  may  be  taken  at  £250  per 


38  Three-Phase  Transmission 

mile.  With  cost  of  copper  at  £65  per  ton,  the  cost  of  the  con- 
ductors for  a  line  of  three  wires  will  be  3  x  609  x  <7  =  ,£1,827  a 
per  mile. 

Assuming  a  line  loss  of  10  per  cent,  and  amount  of  power 
transmitted  10,000  kw.  a  distance  of  150  miles.  The  wasted 

energy  will  be  1,000  kw.,  or  — =  6.65  kw.  per  mile,  and  the 

annual  value  of  this  at  o.25d.  per  unit  is  £60.7  per  annum. 

This  corresponds  to  a  total  capital  cost  for  the  line  of  £405 
per  mile,  allowing  interest  and  depreciation  at  1 5  per  cent. 

The  cost  of  insulation  and  supports  is  £250  per  mile,  leaving 
a  balance  for  the  conductors  of  £155  per  mile. 

If  the  conductors  are  of  copper,  we  have,  therefore, 

-°85  scl-  in< 

The  line  loss  of  6.65  kw.  per  mile  corresponds  to  a  loss  of 
2.22  kw.  per  wire  and  the  resistance  of  a  wire  of  sectional  area  a 
is  per  mile  approximately  : — 

'°42  ,  or  in  this  case  -^"^  =  .495  ohm. 
a  -°°5 


Our  C2R  loss,  therefore,  gives  us  : — 

or  67  amperes. 


/2220 

~V  ^F' 


•495 

Now  the  voltage  V  necessary  to  transmit  10,000  kw.  at 
67  amperes  per  conductor  is  : — 

V^1000,!*1000,  or  80,600  volts. 
^3x67 

The  CR  drop  per  line  wire  is  67x495  =  33.3  volts  per 
mile,  or  for  150  miles  8,660  volts  between  wires,  and  our  per- 
centage line  drop  is  : — 

8660 
_=  ,0.75  per  cent 

The  above  example  illustrates  the  necessity  for  high  voltages 
being  employed  with  power  transmission  over  great  distances  in 
order  to  secure  the  conditions  of  maximum  economy. 

It  may  be  of  interest  to  consider  at  this  point  the  most 
economical  sizes  of  conductors  according  to  Kelvin's  law  with 
extra  high-pressure  transmission  cables. 

If  we  plot  on  squared  paper  the  total  cost  of  laying  similar 


Kelvin's  Law  39 

cables  insulated  for  the  same  working  pressure  with  the  same 
reinstatement  but  having  different  sectional  areas,  we  find  that 
the  corresponding  values  of  total  cost  and  sectional  area  give  us 
points  lying  very  nearly  on  a  straight  line. 

The  total  cost  K  per  mile  in  £  and  the  sectional  area  S  are 
in  fact  for  normal  sections  connected  by  the  law 

K  =  AS  +  B,  where  A  and  B  are  constants. 

Taking  the  cost  of  paper  -  insulated,  lead -covered  and 
armoured  cables  laid  and  jointed  with  those  prices  of  copper 
and  lead  previously  assumed,  we  find  that  the  sectional  areas 
and  cost  per  mile  are  related  to  one  another  approximately  as 
follows  : — 

WORKING  PRESSURE.  COST  IN  £  PER  MILE. 

30,000  K=  10700  S+ 1860 

20,000  K=    71718  +  1200 

10,000  K=    67008+    650 

If  we  denote  by/  the  rate  per  cent,  required  to  cover  interest 
and  depreciation  charges  upon  the  cost  of  the  cables  laid,  that 
part  of  these  charges  per  annum  per  mile  of  cable  which  is 
proportional  to  the  sectional  area  of  the  conductor  is  A/S,  the 
constant  A  being  given  in  the  above  table  for  different  working 
pressures. 

The  cost  of  the  wasted  energy  must  be  considered  as  in- 
volving extra  capital  expenditure  on  plant  and  buildings 
entailed  by  extra  plant  capacity  required  to  supply  this  loss, 
and  the  interest  and  depreciation  charges  upon  such  capital 
must  be  included  in  the  cost  per  unit  of  wasted  energy. 

If  we  assume  a  capital  cost  for  plant  and  buildings  of  £35 
per  kilowatt  and  average  interest  and  depreciation  charges  at 
10  per  cent,  the  annual  cost  under  this  heading  per  unit  per 
annum  is  £3.  IDS. 

The  cost  per  unit  of  wasted  energy  must  also  include  the  net 
running  cost  per  unit  with  the  particular  station  under  considera- 
tion, or  that  cost  strictly  proportional  to  the  number  of  units 
generated.  This  will  depend  upon  the  load  factor,  the  cost  of 
coal  and  other  items  in  any  particular  scheme,  and  must  be 
determined  by  careful  analysis  of  the  total  works  cost  per  unit. 
For  the  present  purpose  we  may  assume  this  to  amount  to 
0.3 5d.  per  kilowatt  hour,  which  corresponds  to  an  annual  cost 


Three-Phase  Transmission 


of  £12.77.     Our  total  cost  per  unit  per  annum  for  wasted  energy 

is,  therefore,  made  up  as  follows  : — 

Capital  charges    -  -     ^3.5 

Running     „  12.7 

Total      -  £16.2 


This  corresponds  to  a  total  charge  of  £12.07  Per  E.H.P. 
per  annum. 

Assuming  that  the  energy  to  be  transmitted  per  single  cable 
is  limited  to  1,000  kw.  under  the  Board  of  Trade  Regulations, 
and  that  this  energy  is  utilised  solely  for  town  lighting  with  a 
13  per  cent,  load  factor,  the  maximum  and  average  currents  per 
conductor  for  various  transmission  pressures  are  given  in  Table 
XIV.,  and  we  may  apply  Kelvin's  law  to  ascertain  the  sectional 
areas  which  will  be  most  economical  under  the  conditions 
assumed.  Thus,  if  we  allow  10  per  cent,  for  interest  and 
depreciation  charges  upon  that  part  of  the  cable  proportional  to 
its  sectional  area,  we  have  for  the  30,000  volt  cable : — 


—  x  6  =  .0048  sq.  in. 


10700  x  10 


TABLE  XIV. 


Transmission 
Pressure. 

Maximum 
Current  per 
Conductor. 

Average 
Current  per 
Conductor. 

Most  Economi- 
cal Section  of 
Conductor. 

Volts. 

Amperes. 

Amperes. 

Square  Inch. 

30,000 

19.2 

6 

.0048 

2O,OOO 

28.9 

9.2 

.009 

IO,OOO 

57-7 

18 

.018 

It  is  interesting  to  note  the  following  points  in  connection 
with  the  above  table  : — 

1.  The  most  economical  average  current  density  is  approxi- 
mately 1,000  amperes  per  square  inch. 

2.  The  sectional  areas  are  too  small  to  be  generally  adopted 
in  practice  on  account  of  mechanical  and  other  considerations. 

3.  The  current  density  at  the  time  of  maximum  load,  which 
would   exceed    3,200   amperes  per  square  inch  with   the   load 
curve  assumed,  would  be  likely  to  cause  damage  to  the  cables 
from  excessive  heating. 


Kelvin's  Law  41 

4.  The  drop  in  pressure  per  mile  of  conductor  at  maximum 
load  would  be  approximately  141  volts,  or  244  volts  between  wires. 

5.  For  a  10  per  cent,  drop  in  the  line,  the  maximum  distance 
under  the  most  economical   transmission   conditions  would  be 
as  follows  : — 

WORKING  PRESSURE  DISTANCE 

IN  VOLTS.  IN  MILES. 
30,000  7.1 

20,000  4.7 

10,000  2.3 

It  will  thus  be  seen  that  the  application  of  Kelvin's  law, 
combined  with  the  limit  of  1,000  kw.  per  cable,  leads  to  results 
which  are  not  commercially  practical  under  the  load  conditions 
assumed. 


CHAPTER    III 
WORKING   PRESSURE 

IN  determining  the  most  suitable  pressure  to  adopt  in  any  parti- 
cular case  we  must  take  into  consideration  the  following  items: — 

1.  The  distance  to  be  covered  by  the  transmission  of  energy. 

2.  The  amount  of  energy  to  be  transmitted. 

3.  The  loss  to  be  allowed  in  the  line  as  governed  by  facilities 
for  regulation  and  the  maintaining  of  constant  pressure  at  the 
receiving  end. 

4.  The  most  economical  size  of  conductor  to  employ,  both  as 
regards  first  cost  and  working  expenses. 

In  connection  with  the  above  items,  it  is  first  to  be  noted 
that  if  we  take  full  advantage  of  the  current  carrying  capacity  of 
any  particular  size  of  cable  as  limited  only  by  the  heating  effect, 
the  C2R  loss  in  the  cable  will  be  in  direct  proportion  to  its 
resistance  and  length,  and  this  loss  will  manifest  itself  by  a  drop 
in  pressure  at  the  receiving  end.  Now  although  we  cannot 
actually  alter  the  amount  of  this  loss  with  a  given  current  and 
section  of  conductor,  we  can  make  it  as  small  a  percentage  of 
the  power  transmitted  as  we  please  by  increasing  the  pressure 
of  transmission.  Thus  in  the  case  of  a  three-core  three-phase 
cable,  if— 

E  =  pressure  between  cores  at  receiving  end  in  volts, 
C  =  current  per  core  in  amperes, 
R  =  resistance  per  core  in  ohms, 
e  =  drop  between  cores  in  volts, 
we  have 

Power  transmitted          W  =  EC  \/3  ( i ) 

Power  lost  in  line  w  =  C2R  x  3  _  (2) 

Drop  in  pressure  on  line  e  =  CR  x  0/3    -  (3) 

It  is  obvious  that  the  ratio  of  the  power  lost  in  the  line  to 
the  power  transmitted  expressed  as  a  percentage  loss  is : — 


Conditions  in  Practice  43 

Similarly  the  efficiency  of  transmission  is  : — 

(E-*)C_    _£ 
EC  E' 

It  will  be  evident  from  the  above  that  the  pressure  may  be 
increased  indefinitely  with  a  corresponding  decrease  in  the  line 
loss  expressed  as  a  percentage  of  the  power  transmitted. 

We  have  already  seen,  from  a  discussion  of  the  line  loss  in 
the  previous  chapter  that  in  practice  the  regulation  to  be  effected 
at  the  generator  end  of  the  line  to  meet  the  percentage  drop  in 
the  line  itself,  the  transformers  at  the  receiving  end,  and  the 
distribution  system  is  generally  strictly  limited,  and,  therefore, 
it  becomes  necessary  to  choose  a  transmission  pressure  which 
will  bring  the  loss  in  pressure  in  the  line,  transformers,  and 
distribution  system  within  these  limits  of  regulation.  Moreover, 
it  will  be  at  once  apparent  that  having  fixed  the  total  line  loss 
or  percentage  drop  in  pressure  to  be  allowed,  this  quantity  ex- 
pressed per  mile  of  cable  over  which  the  transmission  is  effected 
must  correspondingly  decrease  as  the  total  distance  is  increased. 

Taking  the  general  case  met  with  in  practice  we  usually  have 
Amount  of  energy  to  be  transmitted  fixed, 
Distance  fixed, 
Line  loss  limited  by  regulation, 

whereas  our  variables  are 

Current  density  and 
Pressure  of  transmission. 

For  the  purpose  of  rapid  calculation  of  copper  losses  on 
transmission  cables  it  is  convenient  to  remember  the  following 
approximate  relations : — 

(a)  The  resistance  per  statute  mile  of  single  conductor  is 
given  with  close  approximation  by  dividing  the  constant  .0424 
by  the  sectional  area  of  the  core  in  square  inches. 

(&)  With  a  current  density  of  1,000  amperes  per  square  inch 
the  drop  in  pressure  will  be  approximately  i  volt  for  every 
41 1  yards  of  single  core. 

From  equations  (i)  and  (2)  above  we  may  readily  deduce: 
the  following  approximate  relations  : — 

7.4  x  Amperes 
E_   Square  inch    x  Distance  in  miles  _ 

Drop  in  pressure  per  cent. 


44  Three-Phase  Transmission 

Similarly,  if  we  denote  the  power  transmitted  in  kilowatts  by 
K  with  power  factor  P  and  percentage  line  loss  n  we  deduce : — 


p  _      74240  x  K  x  Distance  in  miles  /^v 
\/                    A  x  n  x  P 

.  _  4240  x  K  x  Distance  in  miles  ,  •. 

T79          T> \// 


If  we  require  to  transmit  the  maximum  amount  of  energy  at 
a  minimum  cost  under  the  working  conditions  stated,  we  have 
seen  that  in  practice  the  problem  usually  reduces  itself  to  the 
determination  of  the  relative  values  of  current  density  in  the 
cable  and  pressure  of  transmission.  The  greater  we  make  the 
current  density  the  greater  we  must  make  the  transmission 
pressure  to  keep  the  percentage  line  loss  within  the  regulation 
limit ;  we  shall,  therefore,  require  to  balance  saving  in  cost  of 
copper  against  extra  cost  of  insulation  entailed  by  the  higher 
pressures  adopted. 

If  we  fix  the  power  to  be  transmitted  by  the  cable,  we  must, 
therefore,  vary  the  sectional  area  of  the  cable  and  the  trans- 
mission pressure  to  give  us  the  minimum  of  first  cost  with  the 
given  line  loss  ;  as  will  be  seen  from  equation  (6)  where  E  and  A 
would  be  the  only  variables  under  the  conditions  assumed. 

The  smaller  the  sectional  area  the  less  will  be  the  cost  of 
copper,  but  the  greater  will  be  the  pressure  of  transmission  and 
cost  of  insulation. 

The  curves,  Fig.  7,  based  upon  the  transmission  of  1,000 
kw.  per  cable,  in  accordance  with  the  Board  of  Trade  require- 
ments, at  various  pressures,  and  a  line  loss  of  2  per  cent.,  will 
illustrate  this  point.  It  will  be  seen  that  a  minimum  of  first 
cost  is  obtainable  by  suitably  choosing  the  working  pressure  for 
any  particular  distance  of  transmission. 

It  is  obvious,  however,  that  we  must  consider  the  working 
costs  as  well  as  initial  cost,  to  enable  us  to  finally  select  the 
most  economical  cable  in  practice. 

The  application  of  Kelvin's  law  for  this  purpose  in  its 
ordinary  form  is  not  sufficient,  since  we  have,  in  addition  to  a 
copper  loss  depending  upon  the  sectional  area  of  the  conductor 
and  current  flowing,  a  dielectric  loss,  varying  as  the  square  of 
the  pressure  of  transmission,  and  in  addition  proportional  to  the 
frequency. 

We  see,  however,  that  definite  pressure  limits  exist  in  any 


Minimum  of  First  Cost 


45 


particular  case,  first,  from  consideration  of  initial  capital  cost 
either  for  copper  or  insulation,  secondly,  from  consideration  of 
working  cost  in  connection  with  the  losses  constantly  going  on 
in  the  cable  whilst  energised  both  in  the  dielectric  and  in  the 
copper  due  to  the  charging  current,  even  on  open  circuit. 

The  effect  of  working  pressure  on  the  first  cost  of  the 
cable  is  illustrated  by  the  curves  given  in  Fig.  7.  In  any 
particular  case,  however,  due  consideration  would  have  to 
be  given  also  to  the  increased  cost  of  generating  plant  and 

Cost  of  Cables  Transmitting  1,000  K.W.  with  2  % 
Line  Loss  at  Various  Transmission  Pressures. 


2000 


1000 


<0 

o 

O  5  10  15  20  25  30 

Transmission  Pressure  in  Kilovolts. 

FIG.  7. 

switchgear  as  the  line  pressure  was  raised,  and  in  addition  to  the 
nature  of  the  load  and  safety  in  working  operations. 

As  regards  working  cost,  it  will  be  necessary  to  consider  in 
somewhat  closer  detail  the  order  of  the  losses  to  be  expected  in 
practice. 

At  the  outset  we  are  met  with  a  divergency  of  opinion 
amongst  experimenters  regarding  the  nature  of  the  loss  in  the 
dielectric,  some  asserting  that  this  loss  is  due  to  molecular 
friction  as  in  the  case  of  magnetic  hysteresis,  others  asserting 


46  Three-Phase  Transmission 

Temperature  Test  of  20,000  Volt  Three-Core  7/-095  Cable. 


Temperature  Rise  in  Degrees  Fahr. 

t  *  *.  *  1  ?.  *  *.  1  * 

„ 

X 

X' 

^ 

4 

/ 

7 

^ 

\  ' 

;^"' 

/ 

/ 

x/x 

/ 

/ 

/  ~7 

I 

/' 

// 

/ 

7 

// 

/' 

/ 

/   ^-"^ 

^'' 

54 
2 

i 

/ 

""/ 

/ 

y 

*.,..•?....       •»     ...       .4 

,     4 

5 

r--^ 
~~l« 

Res      in    Ohms 
•?s 

Vi 
k- 

1           -. 

MO                               "Capac 

)                        L                         J 

Farads  per  MTle    3  cores   bunched 
a.      y  i°°         U          i.          l_         " 
Res    m   Megohms  per  Mile 

Time   «  Hours 

FIG.  8. 


that  it  is  due  to  the  resistance  of  the  dielectric  as  a  conductor. 
The  scope  of  the  present  work  will  not  permit  of  a  review  of 
the  arguments  put  forward  by  both  sides.  The  consensus  of 


Annual  Losses  47 

opinion  amongst   those  who   have  experimentally  studied  this 
question  would,  however,  appear  to  be  as  follows  : — 

(1)  With  dielectrics  of  impregnated  paper  and  with  the  range 
of  pressures  at  present  employed  with  these  cables,  the  dielectric 
loss  varies  closely  as  the  square  of  the  effective  pressure,  and 
directly  as  the  frequency. 

(2)  The    dielectric    loss   is   sensitive   to   and   varies    nearly 
directly  with  the  capacity,  and  inversely  as  the  resistance  of  the 
insulator,  when  diminished  by  increase  in  temperature. 

In  connection  with  the  above  the  curves  illustrated  by  Fig.  8 
and  relating  to  a  20,000  volt  cable  may  be  interesting. 

Upon  considering  the  capacities  of  a  number  of  cables  of  the 
same  section  of  conductor,  it  will  be  found  that  there  is  little 
variation  in  the  capacity  as  compared  with  the  working  pressures 
for  which  they  are  constructed.  For  instance,  in  the  case  of  a 
three-core  .04  square  inch  cable  constructed  for  5,000  volts  work- 
ing pressure,  and  a  similar  size  of  cable  constructed  for  20,000 
volts  working  pressure  by  the  same  maker,  the  capacity  of  one 
core  to  two  others  bunched  to  lead  sheath  in  the  latter  cable 
was  found  to  be  66  per  cent,  of  the  former,  and  of  all  three  cores 
bunched  to  lead  sheath  7 1  per  cent,  of  the  former. 

As  the  loss  in  the  dielectric  is  found  to  vary  as  the  capacity 
and  the  square  of  the  working  pressure,  we  may  take  it  that  for 
all  practical  purposes  (in  view  of  the  variation  to  be  found  in 
similar  dielectrics)  the  loss  in  a  transmission  scheme  with  a 
given  size  and  length  of  cable  will  vary  as  the  square  of  the 
working  pressure  we  adopt. 

The  charging  current  may  also  be  considered  as  varying 
directly  as  the  working  pressure.  Take  the  case  of  a  .15  sq. 
in.  11,000  volt  cable,  the  losses  with  an  approximate  sine 
pressure  wave  are  illustrated  by  the  curves,  Fig.  9.  We  see 
that  with  a  3O-mile  length  of  this  cable  the  total  open  circuit 
loss  is  about  10  kw.,  being  made  up  of  6  kw.  in  the  dielectric 
and  4  kw.  in  the  copper.  At  20,000  volts  these  losses  would  be 
approximately  22  kw.  in  the  dielectric  and  1 3  kw.  in  the  copper, 
or  35  kw.  At  a  length  of  little  over  40  miles  the  copper  loss 
exceeds  the  dielectric  loss  and  increases  to  an  enormous  extent 
with  long  cables. 

It  was  stated  in  Chapter  I.  that  with  lighting  load  curves 
having  an  average  load  factor  of  13  per  cent,  for  summer  and 
winter,  the  root  mean  square  value  of  the  load  current  through- 


Three-Phase  Transmission 


out    the  year  was  found  to  be  closely  one-third 


3.22 


of  the 


maximum  current  in  the  same  interval.      We  can,  accordingly, 
11,000  Volt  0-15  sq.  in.  Three-Core  Paper  Cable. 


IA-O 

700 

c/ 

CO 

2 

IOO    <1) 

to 

/ 

/ 

1 

i 

°  4°° 

/ 

B/ 

•M 

x 

7 

/ 

80    £ 

2 

£ 

O    300 

x 

7 

z 

s. 

no  ^ 

/ 

/ 

/ 

no 

E 

ZOO 

/ 

/ 

/ 

|p 

cd 

£ 

/ 

/ 

4O   Q 

IOO 

/ 

x 

/ 

20 

z 

z 

:SS 

• 
o 




/ 

^ 

Jo 

d 

( 

—  • 

io 

—       — 
€ 

_ 
o 

~ 

X) 

Length  in  Miles. 

A  =  Dielectric  Loss.  B  =  Copper  Loss.  C  =  Charging  Current. 

FIG.  9. 

express  the  annual  transmission  loss  directly  as  a  function  of 
the  drop  allowed  in  the  line  at  full  load  with  such  load  curves. 

Upon  the  assumption  that   1,000  kw.  is  the  maximum  load 
to  be  transmitted  by  any  one  cable,  it  is  instructive  to  examine 


Annual  Losses  49 

the  losses  in  copper  and  dielectric  on  transmission  schemes  over 
various  distances  under  these  conditions.  Tables  XV.  and  XVI. 
refer  to  5,000  volt  and  20,000  volt  cables  respectively.  In  the 
case  of  Table  XV.  the  observed  value  of  the  charging  current  over 
a  number  of  miles  of  this  cable  has  been  given.  It  is  nearly 
twice  the  value  which  would  have  been  obtained  with  a  true 
sine  wave. 

In  connection  with  the  annual  loss  in  the  dielectric  given  as 
a  percentage  of  the  units  transmitted,  it  is  of  great  importance 
to  note  that  if  the  maximum  load  had  been  less  than  1,000  kw.,  say 
200  kw.,  the  percentage  losses  would  be  increased  by  five  times. 

It  is,  therefore,  evident  that  to  secure  maximum  economy, 
considerations  which  should  govern  the  working  pressure  to  be 
adopted  should  take  account  of: — 

(a)  Initial  cost  of  cable,  generators,  and  switchgear. 

(£)  Open  circuit  losses  in  the  copper  and  dielectric  of  the 
cable. 

(c)  Load  factor  of  the  demand  at  the  receiving  end. 

The  scope  of  the  present  work  will  not  permit  of  the 
following  up  here  of  this  question  further.  Suffice  it  to  say, 
however,  that  the  transmission  of  electrical  energy  upon  a 
remunerative  basis  can  only  be  effected  by  due  and  proper 
regard  being  given  to  the  issues  indicated  in  the  foregoing 
remarks. 

Breakdown  Strength  of  Dielectrics. — In  connection  with 
the  subject  of  working  pressure,  it  may  not  be  out  of  place  at 
this  stage  to  refresh  our  memories  regarding  some  properties  of 
dielectrics. 

Text-books  on  electrostatics  define  the  unit  of  quantity  of 
electricity  as  a  charge  which,  when  placed  at  a  distance  of  one  cm. 
in  air  from  a  similar  and  equal  quantity,  repels  it  with  a 
mechanical  force  of  one  dyne.  Similarly,  potential  is  measured 
by  the  work  done  in  moving  a  unit  of  +  electricity  against  the 
mechanical  forces  exerted  upon  it,  unit  difference  of  potential 
existing  between  two  points  when  it  requires  the  expenditure  of 
one  erg  of  work  to  bring  a  unit  of  positive  electricity  from  one 
point  to  the  other  against  the  forces  exerted  on  it.  Now,  it  will 
be  remembered  that  work  is  defined  as  the  product  of  force 
by  the  distance  through  which  the  force  is  overcome,  and,  there- 
fore, if  the  difference  of  potential  between  two  points  is  the 
4 


Three-Phase  Transmission 


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52  Three-Phase  Transmission 

work  done  in  moving  a  +unit  from  one  point  to  the  other,  the 
average  electric  force  between  the  points  will  be  found  by 
dividing  the  work  done  by  the  distance  between  the  points. 
That  is  if  Va  and  Vb  are  the  potentials  of  the  inner  and  outer 
conductors  of  a  concentric  cable  with  dielectric  of  thickness  D, 
the  average  electric  force  in  the  dielectric  is — 

Va-Vb 


D 

We  see  from  this  that  as  D  is  diminished  indefinitely  the 
force  becomes  nearly  uniform,  and  the  electric  force  at  a  point 
within  the  dielectric  is  given  by  the  rate  of  change  of  potential 
at  this  point.  Thus  the  resultant  electric  stress  at  a  point  in 
the  dielectric  is  sometimes  termed  the  electric  intensity  or 
potential  gradient. 

Now,  the  result  of  subjecting  any  material  substance  to 
stress  is  to  produce  strain  or  molecular  displacement,  and  if  the 
stress  be  further  increased,  finally  rupture  of  the  material  ensues. 

An  important  difference  between  the  behaviour  of  dielectrics 
subject  to  electrical  stresses  and  materials  subject  to  mechanical 
stresses  must,  however,  be  noted  at  this  point,  and  that  is  the 
property  of  some  dielectrics  to  act  as  electrolytes  or  conductors 
under  excessive  electrical  stresses.  An  interesting  illustration 
of  this  is  the  difference  to  be  found  in  the  sparking  distance 
between  points  and  spheres  subject  to  the  same  voltage.  Owing 
to  a  brush  discharge  occurring  at  much  lower  voltage  between 
needle  points,  the  sparking  distance  between  points  is  greater 
than  between  spheres,  the  explanation  being  that  the  air  sur- 
rounding the  points  is  acting  as  an  electrolyte  or  conductor 
under  the  excessive  electrical  stress,  and  behaves  in  the  same 
manner  as  a  sphere  surrounding  the  needle  point,  thus  for  all 
practical  purposes  reducing  the  distance  between  the  points. 

The  idea  given  by  the  above  illustration  is  of  importance, 
and  when  applied  to  a  cable  with  a  solid  dielectric  we  may 
imagine  the  material  yielding  to  the  pressure  up  to  a  certain 
point  within  it,  thus  acting  as  a  conductor  and  absorbing  energy. 
A  further  interesting  experiment  illustrating  this  point  is  the 
following : — 

If  we  have  two  conductors  separated  by  an  air  space,  and 
an  alternating  difference  of  potential  is  maintained  between 
them  just  below  that  necessary  to  produce  disruptive  discharge, 


Dielectric  Strength  53 

and  some  insulating  material  be  then  introduced  between  them 
having  a  greater  specific  capacity  than  air,  the  air  and  insulating 
material  both  break  down.  The  accepted  explanation  is  that 
since  the  potential  gradient  in  the  air  in  the  first  instance  was 
the  steepest  it  could  withstand,  and  the  increased  specific 
capacity  of  the  insulating  material  causes  the  potential  gradient 
to  be  less  steep  within  it  than  the  air,  the  result  is  an  increase  in 
the  potential  gradient  in  the  remaining  air  space,  which  first 
gives  way  and  is  followed  by  a  breakdown  of  the  insulating 
material. 

The  dielectric  strength  of  an  insulator  may  be  defined  as  the 
greatest  electric  stress  it  can  withstand.  The  dielectric  strength 
of  liquids  and  liquefiable  solids,  such  as  parafifin,  wax,  &c.,  can 
be  readily  determined  by  measurement  of  the  disruptive  voltage 
between  two  equal  spheres  embedded  in  the  material.  In  the 
case  of  paper  and  other  similar  dielectrics,  the  measurement 
of  the  dielectric  strength  presents  some  difficulty.  Sheets  of 
insulating  material  placed  between  metal  electrodes  and  subject 
to  alternating  electric  pressures  cause  the  air  in  the  neighbour- 
hood of  the  electrodes  to  be  ionised,  disturbing  uniformity  in 
the  temperature  of  the  dielectric  and  the  corresponding  maximum 
stress  to  which  it  is  subjected. 

To  fix  our  ideas  we  may  note  the  following  results  obtained 
by  various  experimenters,  the  dielectric  strength  being  expressed 
in  each  case  as  the  potential  gradient  in  kilovolts  per  centimetre 
the  material  will  withstand  : — 

DIELECTRIC.  DIELECTRIC  STRENGTH. 

Manilla  paper  impregnated  with  resin  oil  250 

Paper,  beeswaxed    -  540 

Paper,  paraffined  360 

Resin  oil         •  270-1,350 

Vulcanised  rubber  -  476 

Gutta-percha  -  109 

Air          -         -  27 

Points  of  great  interest  in  connection  with  the  above  are 
that  insulators  which  heat  up  when  subjected  to  alternating 
pressures  do  not  heat  up  when  subjected  to  continuous  pressure, 
also  that  no  brush  discharge  or  hissing  occurs  in  the  neighbour- 
hood of  the  breakdown  stress  if  direct  pressure  be  employed, 
in  addition  that  the  time  the  electric  stress  is  in  operation  largely 


54  Three-Phase  Transmission 

affects  the  result.  For  instance,  presspahn,  5  mm.  in  thickness, 
was  found  to  be  punctured  in  thirty  seconds  with  11,000  volts, 
and  in  two  minutes  fifteen  seconds  with  9,000  volts.  Similarly, 
marble  20  mm.  in  thickness  was  punctured  in  seventy-eight 
seconds  with  20,000  volts,  and  in  two  minutes  by  15,000  volts. 

In  Chapter  I.  reference  was  made  to  the  "  Corona "  effect 
met  with  on  overground  transmission  lines.  It  may  now  be  of 
interest  to  consider  this  point  in  further  detail. 

When  bare  conductors  opposed  to  one  another  are  subject 
to  a  very  high  potential  difference  between  them,  a  faintly 
luminous  glow,  blue  in  colour,  surrounds  them,  and  at  this  stage 
a  loss  of  power  from  atmospheric  dispersion  commences.  If  the 
potential  difference  between  the  conductors  be  still  further 
raised,  a  brush  discharge  occurs  accompanied  by  hissing  and 
the  loss  of  power  greatly  increases.  It  is  important  to  note 
that  this  brush  discharge  takes  place  from  the  exterior  of  the 
luminous  glow  previously  mentioned,  and  not  from  the  surface 
of  the  conductors  themselves.  Experiments  show  that  in  the 
space  occupied  by  the  glow  the  air  is  partially  ruptured,  and  is, 
in  fact,  conducting,  and  that  electrostatic  stresses  in  the  air 
space  between  the  conductors  then  start  from  the  exterior  of 
the  glow.  Further  experiments  point  to  the  fact  that  a 
layer  of  air  immediately  surrounding  a  conductor,  and  which 
is  found  to  vary  in  thickness  with  the  diameter  of  the  con- 
ductor, has  a  resisting  power  to  break  down  many  times  that 
of  the  remaining  air  lying  between  the  conductors.  The 
critical  voltage  of  any  circuit,  or  that  voltage  at  which  the 
"  Corona "  is  produced,  followed  by  a  loss  of  energy  from 
atmospheric  dispersion,  is  found  to  depend  upon  atmospheric 
conditions  such  as  barometric  pressure,  humidity,  and  others 
which  have  probably  not  yet  been  investigated.  The  critical 
voltage  of  the  circuit  also  becomes  higher  as  the  diameter  of  the 
wires  and  their  distance  apart  are  increased,  but  the  effect  of 
increasing  the  spacing  of  the  wires  upon  the  critical  voltage 
quickly  reaches  a  limit,  and  any  further  spacing  is  practically 
ineffective  in  preventing  the  formation  of  the  "  Corona."  It  has 
been  found  that  whilst  the  effect  of  rain  is  small,  yet  the 
presence  of  fog,  smoke,  and  particles  in  suspension  in  the 
atmosphere  largely  increase  the  losses.  Further,  these  depend 
in  every  case  upon  the  maximum  value  of  the  voltage  wave, 
and  also  to  some  extent  upon  the  frequency  of  the  circuit. 


Atmospheric  Dispersion  55 

Some   observed   atmospheric    losses   on   different   lines   are 
given  below  : — 

TABLE  XVII. 


Diameter 
of  Wires. 

Distance  apart 
of  Wires. 

Effective  Work- 
ing Pressure. 

Loss  per 
Mile. 

Inch. 

Inches. 

Volts. 

Kilowatts. 

.325 

84 

IIO,OOO 

3 

.325 

52 

58,000 

0.89 

•325 

35 

51,000 

0.22 

The  "  Corona "  effect  has  been  investigated  by  Ryan  and 
Mershon  in  America,  but  the  results  obtained  by  these  experi- 
menters show  considerable  discrepancies. 

Kapp  gives  the  following  formula  based  upon  Mershon's 
results  for  the  critical  potential  difference  in  virtual  kilovolts 
between  two  parallel  wires  : — 


K.V.-: 


0.5  +r    \i  +0.013 


r  log.  1 


where 


b  =  barometric  pressure  in  millimetres  of  mercury. 
r  =  radius  of  wire,  centimetres. 
s  =••  distance  between  wires  in  centimetres. 
v=  Mershon's  vapour   product  or   the    pressure    of   saturated 
steam  in  millimetres  of  mercury  at  the  given  temperature 
multiplied  by  the  relative  humidity  or  the  ratio 
actual  moisture 
possible  moisture' 

Curves  based  upon  this  formula,  giving  critical  pressure  for 
wires  of  various  diameters  spaced  at  different  distances  apart, 
are  plotted  in  Fig.  10. 

It  would  appear  necessary,  however,  to  employ  a  factor  of 
safety  of  at  least  two  with  these  results  where  the  wires  pass 
in  the  neighbourhood  of  towns  or  industrial  districts. 

It  is  further  to  be  noted  that  dispersion  loss  from  the  wires, 
depending  as  it  does  upon  their  spacing  in  air,  will  be  likely  to 
be  increased  at  the  points  of  suspension  where  steel  towers  are 
employed,  the  air  space  between  the  wires  being  less  in  the 
neighbourhood  of  the  metal  tower  than  at  other  points  along 
the  span. 


Three-Phase  Transmission 

DISTANCE    BETWEEN    WIRES— FEET. 


S     eo 


CRITICAL    PRESSURE    BETWEEN    WIRES— 
KILOVOLTS. 


Line  Regulation 


57 


LOAD  CURRENT  IN  AMPERES 


40          50          60          70 


FIG.  ii. 


58  Three-Phase  Transmission 

Line  Regulation. 

In  the  western  parts  of  America  the  high  frequency  of  60 
cycles,  which  is  common  there,  gives  rise  to  very  heavy  capacity 
currents  at  the  high  working  pressures  adopted. 

The  effect  of  these  capacity  currents  upon  the  regulation  for 
constant  pressure  at  the  receiving  end  of  the  line  is  very  marked 
in  some  cases.  For  instance,  it  may  happen  that  the  current 
entering  the  line  at  the  sending  end  may  decrease  with  increase 
of  load.  Further,  that  the  generator  pressure  at  the  sending 
end  will,  under  some  conditions,  be  less  than  the  pressure  at  the 
receiving  end  of  the  line.  Some  of  these  effects  are  illustrated 
by  the  curves  given  in  Fig.  n. 

In  the  figure  the  voltage  V^  between  each  phase  and  neutral 
point  of  the  generator  required  to  maintain  the  constant  voltage 
V,  at  the  receiving  end  of  a  feeder  50  miles  in  length,  with 
different  loads  and  power  factors,  is  given  by  the  upper  curves. 
The  current  A^  supplied  to  the  line  by  the  generator  under  the 
conditions  of  different  loads  and  power  factors  is  given  by  the 
lower  curves. 

A  simple  and  rapid  method  which  may  be  adopted  for 
estimating  such  effects  with  any  given  transmission  scheme  will 
be  found  in  Appendix  D. 


CHAPTER  IV 
THE   CONTROL   OF    E.H.P.   TRUNK    MAINS 

Switchboard  Construction. — With  the  rapid  growth  of 
electricity  supply  systems  and  the  enormous  outputs  of 
modern  power  stations,  the  necessity  for  absolute  continuity  in 
the  supply  has  become  of  the  greatest  importance.  The 
possibility  of  a  complete  shut  down  of  the  whole  supply  as 
the  result  of  a  single  fault  upon  a  main  switchboard  such  as 
the  failure  of  an  oil  switch,  a  temporary  short  circuit  to  frame 
or  between  conductors,  can,  in  view  of  such  requirements,  no 
longer  be  permitted.  The  complete  destruction  by  fire  in  some 
cases  of  congested  types  of  switchboards  comprising  generator, 
feeder  and  section  panels  all  crowded  into  the  minimum  possible 
space,  and  formerly  so  general,  has  demonstrated  the  necessity 
for  very  wide  subdivision  of  the  controlling  switchgear  where 
large  amounts  of  power  have  to  be  dealt  with.  Accordingly, 
the  generator,  feeder,  and  section  panels  comprising  a  modern 
switchboard  are  usually  so  widely  separated  individually  and 
collectively,  that  the  spread  of  fire  is  effectively  limited  to  the 
faulty  section,  and  thus  disorganisation  of  the  supply,  in  the 
event  of  a  fault,  reduced  to  a  minimum. 

Such  wide  subdivision  involves  the  use  of  remote  control 
switchgear  in  order  that  distant  switches  may  be  promptly 
operated  from  a  keyboard  situated  at  some  convenient  central 
point.  The  remote  control  systems  in  most  general  use  are : — 
(i)  Electrically  operated  ;  (2)  Mechanically  operated. 

In  America  electrical  control  is  largely  adopted,  and  this 
system  has  also  been  installed  with  important  plants  in  this 
country.  Mechanical  control  has,  however,  been  extensively 
used  upon  the  Continent  with  remote  switchgear. 

On  account  of  the  considerable  weight  of  the  high-power  oil 
switches  required  in  modern  generating  stations  and  the  long 
break  necessary,  trouble  has  sometimes  been  experienced  in  the 
closing  of  such  switches  with  sufficient  rapidity  for  synchronising 


6o  Three-Phase  Transmission 

purposes  where  mechanically  operated  remote  control  has  been 
installed.  With  electrical  control  the  action  of  the  switch  may 
be  made  very  prompt,  and  is  unaffected  by  the  distance  the 
switch  is  situated  from  the  control  desk  of  the  operator.  It  is  to 
be  specially  noted  that  any  feeder  switch  in  connection  with  the 
main  bus  bars  of  the  generating  station  may,  under  the  condi- 
tions of  a  short  circuit,  have  to  break  the  total  output  of  the 
plant  running  at  the  time  quite  irrespective  of  the  normal  load 
the  feeder  will  carry.  The  advantage  of  having  such  switches 
installed  with  plenty  of  space  and  at  a  distance  from  the 
operator  is  obvious,  and  it  is  now  quite  common  with  high- 
power  generating  stations  to  find  a  complete  side  or  end  of  the 
building  partitioned  off  for  the  installation  of  switchgear,  often 
occupying  three  or  more  floors.  The  arrangement  of  switchgear 
and  transformers  illustrated  by  Fig.  12  was  installed  by  the 
Oerlikon  Company  in  a  Continental  generating  station  feeding 
five  overground  transmission  lines  at  a  pressure  of  33,000  volts 
between  wires.  Bare  copper  conductors  from  each  6,ooo-volt 
three-phase  generator  enter  the  switchgear  annexe  at  the  point 
A,  and  are  brought  to  electrically  operated  oil  switches  B,  fitted 
with  maximum  reverse  relays.  From  this  point  connections  are 
made  through  current  transformers  to  change-over  oil  switches 
E,  permitting  of  each  generator  being  coupled  to  the  6,ooo-volt 
bus  bars  shown,  or  alternatively  to  the  primaries  of  one  group  of 
three  delta-connected  transformers  G.  The  secondary  connec- 
tions to  these  transformers  are  brought  through  oil  switches  J, 
fitted  with  maximum  relays,  to  33,ooo-volt  ring  bus  bars  at  M. 
From  these  bus  bars  each  set  of  feeder  connections  passes 
through  electrically  operated  oil  switches  O  and  choke  coils  Q 
to  the  transmission  lines  leaving  the  building  at  R.  Switches 
for  isolating  the  lines  are  shown  at  S  and  lightning  arresters  at  T 
in  series  with  water  resistances  U. 

Situated  upon  a  platform  overlooking  the  engine-room  is  a 
main  switchboard  w,  controlling  the  transformer  and  line 
switches,  and  at  V  are  pillars  for  operating  the  generator 
switches  whilst  facing  the  engine-room. 

As  will  be  seen  from  Fig.  12,  the  cellular  system  of  switch- 
gear  has  been  adopted,  the  switchboards  being  constructed  of 
incombustible  material  with  horizontal  and  vertical  partitions 
separating  conductors.  No  additional  precautions,  however,  are 
taken  to  screen  live  parts,  but  the  rooms  in  which  these  are 


Continental  Switchgear 


6  i 


situated  are  locked  off  from  the  rest  of  the  station,  and  access  to 
them  on  the  part  of  all  but  skilled  assistants  is  forbidden.  It 
will  further  be  noticed  that  no  high-pressure  connections  are 
brought  on  to  the  operating  platform. 


FIG.  12. 


The  arrangement  of  a  bus  bar  room  with  Continental  type 
switchgear  is  illustrated  by  Fig.  13. 

As  a  typical  arrangement  of  high-power  British  switchgear 


62  Three-Phase  Transmission 

we  may  take  an  installation  by  Messrs  Ferranti  where  the  feeders 
consist  of  underground  cables  and  the  following  disposition  of 
the  gear  is  adopted.  The  generator  and  feeder  panels  are  placed 


FIG.  13. 

upon  opposite  sides  of  a  brick  wall  passing  upwards  through 
three  or  more  floors  of  the  building.  On  the  first  floor  are 
situated  the  cable  receivers,  from  which  point  the  connections 


British  Switchgear  63 

of  each  phase  pass  upwards,  separated  by  incombustible  parti- 
tions forming  with  horizontal  partitions  tiers  of  cells  containing 
the  isolating  switches,  spark  gaps,  current  and  potential  trans- 


Fio.  14. 


formers.  The  connections  then  pass  through  porcelain  insu- 
lators to  the  second  floor,  upon  which  are  placed  the  main 
electrically  controlled  oil  switches.  After  traversing  these 
switches  the  connections  are  brought  upwards  to  a  further 


64  Three-Phase  Transmission 

set  of  isolating  switches,  enabling  each  generator  or  feeder  to 
be  coupled  to  either  of  two  sets  of  bus  bars  arranged  in  ring 
form  and  situated  on  the  third  floor. 

Fig.  14  illustrates  the  arrangement  of  a  main  switch  floor, 
and  shows  the  electrically  operated  switches  disposed  in  brick 
cells  with  the  isolating  switches  above  them. 

Each  floor  containing  extra  high-pressure  switchgear  is 
locked  off  by  doors  from  the  remainder  of  the  building,  but 
everything  is  readily  accessible  to  authorised  persons  entering 
the  enclosures,  upon  the  removal  of  light  sheet-iron  covers 
screening  the  cubicles  and  bus  bar  chambers.  The  whole  of 
the  electrically  operated  switchgear  is  controlled  from  a  working 
platform  overlooking  the  engine-room,  upon  which  everything  is 
safe  to  handle. 

In  the  case  of  switchgear  situated  in  substations  at  the 
receiving  ends  of  lines  or  feeders,  the  working  conditions  are 
somewhat  different  to  those  at  the  generating  station.  Space 
will  often  be  restricted,  demanding  more  or  less  concentration 
of  the  switchgear ;  in  addition,  greater  precautions  will  gene- 
rally be  necessary  to  protect  the  substation  attendants  from 
accidental  contact  with  live  parts.  Since  the  effect  of  short 
circuits  will  not  be  so  disastrous  at  the  receiving  ends  of  long 
feeders  adequately  protected  at  the  generating  station,  it  will 
generally  be  permissible  to  adopt  self-contained  designs  of 
switchgear.  At  the  same  time,  well-recognised  principles  must 
be  borne  in  mind,  and  a  brief  review  of  some  types  of  substation 
switchboards  at  present  in  use  may  not  be  out  of  place  at  this 
stage. 

These  may  be  classed  as  follows  : — 

(1)  Enclosed  cell  or  cubicle  type,  frame  of  brick,  slate,  or 
concrete,  without  space  at  the  back. 

(2)  Flat  type  with  space  at  the  back,  framework  of  metal, 
screening  live  fittings,  or  separate  locked  chambers  enclosing 
exposed  live  fittings. 

(3)  Ironclad  or   solid  type,  frame   of  iron  or   other   metal 
enclosing  all  live  parts,  the  space  between  being  filled  up  solid 
with  insulating  compound  or  material. 

The  conditions  to  be  aimed  at  in  the  construction  of  a 
substation  switchboard  are,  in  relative  order  of  importance,  it 
is  suggested,  as  follows  : — 

(a)  The  absence  of  danger  to  the  life  of  the  operator. 


Substation  Switchgear  65 

(£)  Freedom  from  breakdown  and  effective  restriction  to  the 
spread  of  fire. 

(c)  Reasonable  initial  cost. 

Considering  first  the  most  important  object  to  be  attained, 
viz.,  safety  to  human  life,  it  may  be  noted  that  the  possibilities 
of  the  operator  obtaining  fatal  shocks  are  (i)  the  forming  of  a 
path  through  his  body  or  portion  thereof  for  an  E.H.P.  discharge 
between  live  metal  at  different  potentials ;  (2)  the  forming  of  a 
path  through  his  body  or  portions  thereof  for  a  discharge  from 
live  metal  to  metal  or  other  material  at  earth  potential. 

In  general  a  discharge  through  the  body  of  the  operator  to 
earth  would  be  effectually  guarded  against  if  the  material  used 
in  the  construction  of  the  switchboard  frame  was  possessed  of 
sufficiently  insulating  qualities  added  to  the  adoption  of  rubber 
mats  upon  the  operating  platform.  A  difficulty  arises,  however, 
from  the  fact  that  slate,  concrete,  brickwork,  and  other  materials 
commercially  adaptable  for  switchboard  construction  are  not 
only  in  themselves  possessed  of  insufficiently  insulating  qualities 
to  prove  a  safeguard  to  life  in  cases  of  leakage,  such  as  that  due 
to  a  broken  insulator  permitting  live  metal  at  extra  high  pressure 
to  come  in  contact  with  or  discharge  to  them,  but  in  addition 
such  materials  will  of  themselves  pass  a  sufficient  current  at 
extra  high  pressures  to  fire  inflammable  insulating  materials  in 
their  vicinity.  From  this  it  is  sometimes  argued  that  imperfect 
insulating  material  used  to  screen  live  metal  is  worse  than  bare 
live  metal  itself  in  at  least  that  there  is  no  guise  of  safety. 

Accordingly,  a  frame  of  iron  or  other  metal  effectively 
earthed  is  now  frequently  employed  to  screen  extra  high- 
pressure  switchboard  panels,  and  bare  copper  conductors  sup- 
ported upon  porcelain  insulators  are  used  in  place  of  rubber  or 
tape  insulated  connections. 

The  adoption  of  this  course  completely  shields  the  operator 
from  the  danger  of  high  resistance  leaks  and  the  charging  of 
isolated  metal  parts  thereby.  It  ensures  also  that  the  develop- 
ment of  a  fault  will  be  promptly  followed  by  a  direct  discharge 
to  the  earthed  framework  of  the  switchboard. 

In  the  absence  of  adequate  subdivision  of  the  feeder  panels, 
however,  a  discharge  to  frame  would  be  likely  to  result  in  a  shut 
down  of  the  supply,  and  unless  each  panel  be  so  arranged  that 
access  to  the  connections  shielded  by  the  metal  frame  cannot 
be  gained  whilst  the  panel  is  live,  an  increased  risk  of  accidental 
5 


66  Three-Phase  Transmission 

contact  on  the  part  of  the  operator  between  live  metal  parts  and 
the  earthed  frame  of  the  switchboard  will  exist. 

In  connection  with  this  point  must  be  mentioned  a  novel 
departure  from  the  general  lines  upon  which  switchboards  have 
for  many  years  been  constructed.  This  refers  to  the  ironclad 
type  of  svvitchgear  introduced  by  Messrs  Reyrolle  &  Co.  In 
this  type  the  bus  bars  are  enclosed  in  a  longitudinal  cast-iron 
case  filled  in  solid  with  compound.  Each  feeder  cable  is 


FIG.  15. 

terminated  by  a  cast-iron  dividing  box  to  which  is  attached 
directly  a  further  casing  containing  current  transformers  and 
situated  immediately  below  the  bus  bar  chamber. 

Plug  sockets  are  arranged  with  suitable  centres  in  the  bus 
bar  chamber  and  transformer  casing  respectively. 

An  oil  switch  in  the  form  of  a  carriage  and  provided  with 
external  contacts  is  supported  by  a  framework  and  plugs  into 
the  sockets  formed  in  the  bus  bar  chamber  and  transformer 
casing,  thus  completing  the  circuit  between  the  feeder  cable  and 


Ironclad  Switchgear  67 

bus  bars.     This  type  of  switchgear  is  illustrated   by  Figs.   15 
and  1 6. 

By    this    arrangement    all     concrete    and     brickwork    are 


FIG.  1 6. 


eliminated,  isolating  switches  are  unnecessary,  and  instrument 
connections  rendered  as  short  as  possible.  Other  important 
features  are  that  the  amount  of  cleaning  of  live  parts,  insulators, 


68 


Three- Phase  Transmission 


&c.,  is  reduced  to  a  minimum.     Spare  switches  can  be  carried, 
and  duplicate  bus  bar  chambers  readily  arranged  if  desired. 

Coming  now  to  condition  (<£),  z'.<?.,  freedom  from  breakdown 
and  restriction  to  the  spread  of  fire  if  started,  one  of  the  most 
important  points  in  the  writer's  experience  is  the  avoidance 
of  rubber  insulated  cable  connections  upon  the  switchboard. 
Rubber  under  the  influence  of  ozone,  always  present  in  more  or 
less  quantities  in  the  neighbourhood  of  extra  high-pressure 
switchgear,  is  rapidly  perished  and  rendered  useless  both 


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GENERATORS 


FIG.  17. 


electrically  and  mechanically,  and  will  readily  start  a  fire  under 
such  conditions. 

The  general  subdivision  of  phases  starting  from  the  cable 
receiver  itself  is  highly  desirable,  but  will  add  considerably  to 
the  cost  of  the  switchgear,  and  with  a  brick  or  concrete  frame- 
work generally  involves  deep  and  narrow  cells,  which  render 
access  to  connections  for  repairs  and  cleaning  difficult. 

The  cubicle  system  carried  out  completely  in  brickwork  or 
artificial  stone,  however,  is  capable  of  withstanding  for  some 


Arrangement  of  Bus  Bars 


69 


time  the  high  temperature  of  heavy  current  arcs  under  the 
conditions'  of  short  circuit,  which  may  allow  of  a  fault  clearing 
itself  if  the  oil  switches  are  capable,  as  they  should  be,  of  break- 
ing the  short  circuit  current. 


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With  duplicate  feeders  to  each  substation  fed  from  inde- 
pendent switchboard  sections  an  extensive  interruption  within 
the  supply  area  is  rendered  a  very  remote  contingency. 

As  regards  condition  (c\  i.e.,  that  of  reasonable  cost,  it  is  to 


70  Three-Phase  Transmission 

be  noted  that  the  use  of  an  iron  frame  will  largely  cheapen  the 
design  of  a  switchboard.  It  must  be  remembered,  however,  that 
flat  type  switchboards  with  live  connections  exposed  at  the 
back  were  at  one  time  largely  used  in  this  country,  but  were 
subsequently  abandoned  on  the  score  of  danger  to  the  operator. 
It  is  very  difficult  to  estimate  the  ultimate  pecuniary  loss 
accruing  to  an  electricity  supply  undertaking  as  the  result  of  a 
breakdown,  but  the  more  extensive  and  important  the  field 
covered  by  the  undertaking,  so  much  more  surely  will  additional 
capital  expenditure  upon  the  score  of  safety  and  reliability  be 
justified. 

Some  typical  arrangements  of  bus  bars,  generator,  and  feeder 
circuits  are  illustrated  by  Figs.  17  and  18. 

Where  a  number  of  trunk  mains  enter  a  distributing  station 
from  which  radiate  a  number  of  subfeeders  to  various  sub- 
stations, some  important  considerations  arise. 

If  trunk  mains  and  feeders  are  coupled  up  to  ring  bus  bars 
and  worked  undivided,  a  single  fault  upon  the  switchboard  will 
usually  mean  a  total  shut  down  of  the  supply. 

By  allocating  to  certain  trunk  mains  definite  sections  of  the 
ring  bus  bars  and  their  feeder  circuits  the  effect  of  a  fault  is 
limited  to  a  particular  section,  but  the  convenience  of  running 
with  the  trunk  mains  in  parallel  and  equally  loaded  is  lost. 

A  further  possible  arrangement  is  to  parallel  all  the  trunk 
mains  on  to  an  independent  set  of  auxiliary  bus  bars  to  which 
sections  of  the  ring  bus  bars  with  their  feeders  are  coupled 
through  maximum  automatic  switches.  This  allows  of  all  trunk 
mains  being  run  in  parallel,  and  also  limits  the  possibility  of  a 
total  shut  down  of  the  supply. 

It  is,  however,  difficult  even  in  this  case  to  provide  against 
all  eventualities.  For  instance,  should  it  happen  that  a  fault 
occurred  upon  a  feeder  section  of  the  switchboard  at  time  of 
light  load,  the  automatic  switches  on  one  or  more  small 
generators  working  at  the  time  might  be  opened  before  the 
switch  on  the  bus  bar  section  upon  which  the  fault  occurred, 
thus  causing  a  complete  interruption  in  the  supply. 

The  Merz-Price  balanced  system  of  protection,  to  be  described 
later,  might,  with  some  modifications,  be  adapted  to  meet  most 
working  conditions  in  the  sectionalising  of  large  switchboards, 
and  ensure  that  a  minimum  portion  of  the  supply  was  inter- 
rupted in  the  event  of  a  fault  occurring  upon  any  particular  panel. 


Oil  Break  Switches 


FIG.  19. 

Switches. — The  development  of  the  oil  type  of  E.H.P. 
switch  and  the  satisfactory  manner  in  which  such  switches  are 
found  to  operate  upon  E.H.P.  alternating  current  circuits 


72  Three-Phase  Transmission 

possessing  self-induction  and  capacity,  has  rendered  working 
pressures  possible  with  safety  which  would  hitherto  have  been 
associated  with  considerable  risk  to  the  cable  system  from  surges 
and  pressure  rises  attendant  upon  the  use  of  air  break  switches. 
Oil  break  switches,  although  they  may  be  relied  upon  to  open 
E.H.P.  alternating  current  circuits  with  safety,  have  no  re- 
straining influence  upon  the  pressure  rises  due  to  the  closing 
of  the  circuit.  Oscillograph  records  show  that  pressure  waves 
of  about  twice  the  normal  amplitude  may  occur  under  such 
conditions. 

Types  of  high-power  British  and  Continental  switches  are 
illustrated  by  Figs.  19  and  20  respectively.  Fig.  19  illustrates 
the  Ferranti-Field  type  of  electrically  operated  oil  switch  for 
normal  working  pressure  of  10,000  volts  and  10,000  kw. 
capacity.  For  higher  voltages,  three  separate  single-phase 
switches  are  used,  each  situated  in  its  own  cell,  but  all  coupled 
to  a  single  shaft  operated  by  the  solenoid  surmounting  the 
switch  as  in  Fig.  19.  By  employing  the  direct  vertical  pull 
of  a  powerful  solenoid  to  operate  the  switch,  complication  is 
avoided.  The  switch  is  held  closed  by  a  double  scissor  arrange- 
ment of  links,  and  the  tripping  solenoid  shown  to  the  right  of 
the  figure  allows  the  links  to  collapse  and  opens  the  switch 
under  the  action  of  gravity  assisted  by  spiral  springs.  On  the 
left  of  the  figure  will  be  seen  a  small  barrel-type  contactor  for 
indicating  by  means  of  signal  lamps  whether  the  switch  is  open 
or  closed. 

Fig.  20  illustrates  an  Oerlikon  type  of  mechanically-con- 
trolled switch.  For  pressures  of  30,000  volts  and  upwards  the 
three  double-break  switches  of  which  it  is  composed  are  in- 
stalled in  separate  cells.  These  switches  are  sometimes  operated 
from  a  distance  electro-magnetically,  in  other  cases  by  means  of 
grooved  wheels  and  rope  gear. 

Before  discussing  in  detail  automatic  devices  including  trip 
coils,  time  element  relays,  &c.,  as  generally  applied  to  E.H.P.  oil 
switches,  it  may  be  advisable  to  consider  some  of  the  conditions 
which  have  to  be  met  in  practice  by  such  apparatus. 

The  necessity  for  ensuring  the  continuity  of  the  supply,  and 
the  Board  of  Trade  Regulations  restricting  the  total  amount  of 
energy  to  be  transmitted  by  any  one  cable,  result  in  the  use  of 
at  least  two  or  more  cables  in  parallel  under  normal  conditions 
in  practice.  As  will  be  shown  in  what  follows,  the  use  of  a 


Oil  Break  Switches 


73 


FIG.  20. 


number  of  cables  in  parallel  and  the  methods  to  be  adopted  to 
suitably  protect  them  and  control  their  working  with  due  regard 


74 


Three-Phase  Transmission 


to  continuity  in  the  supply  of  energy  transmitted,  involve  some 
special'  considerations. 

One  point  which  is  at  once  obvious  is  that  if  we  have  a  star- 
wound   generator   with   earthed    neutral    point   supplying    two 
feeders  in  parallel  at  the  bus  bar  A 
^  (Fig.  21),  and   provided  with  equal 

— — f — f—^ fuses  Fp  F2,  F3,  F4,  at  the  generator 

3  and  receiving  ends  of  the  line  A  and 

B  respectively,  then  if  a  fault  occurs 
at  E,  fuse  F3  will  first  blow,  being  in 
the  path  of  least  resistance  to  the 
fault.  This  fuse  will  be  followed 
by  the  blowing  of  fuses  ¥l  and  F.,, 
-^.  C.  since  these,  in  addition  to  having  to 
carry  the  total  load  being  trans- 
mitted, have  to  carry  the  current 
through  the  fault  by  way  of  F1%  F.,, 
F4,  and  E. 

It  is  important  to  note  that  as 
we  increase  the  number  of  feeders 
*  in  parallel,  the  danger  of  a  fault 
upon  one  feeder  resulting  in  a  total 
cessation  of  the  supply  may  be 
avoided  by  suitably  choosing  the 


B 

FIG.  21. 


overloads  at  which  the  fuses  will  act. 

The  general  case  may  be  stated  thus  :  — 

Let  L///  =  Maximum  load  in  kilowatts  carried  by  any  trunk  feeder. 
r=  Overload  required  to  blow  each  fuse  in  per  cent,  -f-  100. 
n  =  Number  of  trunk  feeders. 

Then  the  total  load  required  to  operate  any  fuse  is  :  — 
r   Kw. 


With  one  feeder  cut  out,  the  load  on  each  of  the  remaining 
(n—  i)  feeders  is  increased  to  — 

L»i—         .  Kw. 

n  —  i 

Therefore  the  margin  before  the  (n—  i)  fuses  operate  is  :  — 
Lm(n~i) 


Feeders  in  Parallel  75 

and  this  must  be  greater  than  : — 

tm(i+r) 

.  •.     (n  -  i )  ( r  +  r)  -  n  >  i  +  r 

or  r>—?-  . 

n  —  2 

Applying  the  condition  for  safety,  i.e.,  r>  — - — ,  to  different 

numbers  of  feeders  in  parallel,  we  obtain  values  for  the  overload 
setting  of  the  fuses  as  follows  : — 

n  r 

2  a 

3  2 

4  i 

5  0-6 

6  0.5 
8  0.3 

10  0.25 

Thus  with  four  feeders  the  overload  would  be  100  per  cent, 
with  six  feeders  50  per  cent.,  and  with  ten  feeders  only  25  per 
cent,  for  safety  under  the  conditions  of  the  fault  assumed. 

It  will  be  obvious  that  the  same  law  must  govern  the  setting 
of  simple  maximum  type  automatic  switches  or  cut  outs.  Auto- 
matic devices,  however,  allow  of  the  case  considered  being  treated 
in  other  ways. 

As  oil  break  switches  became  more  generally  used  with 
high-pressure  alternating  current  schemes,  and  the  electrical 
advantages  of  the  oil  break  became  more  fully  understood, 
fuses  were  replaced  by  automatic  attachments  to  the  oil 
switches.  It  soon  became  evident,  however,  that  an  important 
feature  which  most  types  of  fuses  possessed  in  having  a  "  time 
element "  was  in  many  cases  still  desirable  with  automatically 
operated  oil  switches.  This  led  to  the  design  of  numerous 
devices  which  have  now  become  familiar  under  the  title  of 
inverse  time  element  relays  or  time  limit  relays.  The  control 
of  automatic  oil  switches  by  such  devices  generally  involves  the 
use  of  three  distinct  pieces  of  apparatus. 

1.  Current  transformer. 

2.  Relay  with  time  element. 

3.  Trip  coil. 

In  some  cases,  also,  an  auxiliary  source  of  power  such  as  a 


76  Three-Phase  Transmission 

battery  is  required  to  operate  the  trip  coil,  this  being  brought 
into  circuit  by  the  relay. 

The  current  transformer  has  two  principal  functions.  It 
insulates  effectively  the  high-pressure  system  from  the  relay 
and  trip  coil  mechanism,  enabling  the  latter  together  with  the 
necessary  measuring  instruments  to  be  actuated  at  low  voltage. 

In  addition,  it  enables  a  standard  type  of  relay,  trip  coil, 
ammeter,  &c.,  to  be  adopted  upon  circuits  carrying  currents 
differing  very  largely  in  magnitude.  The  usual  practice  is  to 
wind  the  current  transformers  with  a  few  standard  ratios  which 
give  a  fixed  secondary  current  of  from  8-10  amperes  at  the  full 
load  range  of  primary  currents  usually  met  with. 

The  function  of  the  relay  is  to  throw  into  circuit  the  trip  coil 
when  a  predetermined  overload  has  been  reached,  and  after  the 
lapse  of  a  time  interval  inversely  proportional  to  the  magnitude 
of  the  overload  when  this  is  maintained. 

The  trip  coil,  as  its  name  implies,  usually  actuates  an  arma- 
ture, which  by  its  movement  trips  a  catch  holding  the  oil  switch 
in  its  "  on "  position,  the  switch  being  then  opened  by  gravity 
or  springs. 

One  of  the  simplest  types  of  current  transformer  is  con- 
structed in  the  form  of  a  ring  of  iron  stampings  upon  which  is 
wound  the  secondary  or  low  voltage  winding.  This  ring  is 
slipped  over  a  porcelain  insulator  through  which  a  copper  rod 
passes,  carrying  the  high-pressure  current  which  is  made  to 
form  the  primary  of  the  transformer. 


Relays. 

An  early  form  of  relay  used  with  automatic  switches 
for  introducing  a  time  element  consisted  of  a  solenoid  com- 
bined with  a  dashpot.  The  piston  of  the  dashpot  was 
formed  of  a  double  bell  submerged  in  mercury  and  oil.  If  a 
short  circuit  occurred  the  mercury  and  oil  contained  in  the 
lower  and  upper  half  of  the  piston  respectively  were  lifted 
bodily,  and  the  action  of  the  relay  was  instantaneous.  With 
an  ordinary  overload,  however,  the  pull  upon  the  plunger  would 
regulate  the  time  taken  for  the  oil  to  pass  from  the  upper 
to  the  lower  portion  of  the  bell  through  a  small  hole  in  the 
diaphragm,  and  thus  allow  the  plunger  to  rise  and  complete  the 
trip  coil  circuit. 


Inverse  Time  Element 


77 


This  type  of  solenoid  relay  was  found  to  possess  many 
defects  in  practice. 

After  the  plunger  had  once  risen  with  an  overload  and  the 
current  then  fell  the  plunger  remained  in  a  higher  position  than 
that  originally  corresponding  to  the  current  passing.  If  a  second 
overload  then  occurred  the  time  element  was  impaired  if  not 
altogether  wiped  out. 

A  further  trouble 
sometimes  arose  from 
the  fact  that  the  impe- 
dance of  the  coil  varied 
with  the  position  of  the 
plunger,  the  choking 
effect  increasing  as  the 
plunger  rose  in  the 
solenoid. 

Some  solenoid  and 
plunger  types  of  trip 
coil  also  suffer  from 
similar  defects.  With 
a  gradually  increasing 
overload  the  plunger 
may  creep  up  the  sole- 
noid until  it  comes  in 
contact  with  the  trip 
lever.  A  much  greater 
overload  is  then  required 
to  operate  the  trip  than 
if  this  were  applied  sud- 
denly, owing  to  the  ab- 
sence of  the  inertia 
gained  by  the  plunger 
by  a  rapid  upward 

movement,  which  would  otherwise  ensure  the  knocking  off  of 
the  trip.  With  intermittent  overloads,  therefore,  considerable 
care  must  be  exercised  in  the  selection  of  a  solenoid  type  of 
relay  or  trip  coil  to  ensure  satisfactory  working. 

The  relay  has  been  omitted  altogether  by  some  manu- 
facturers, a  time  element  being  provided  instead,  by  means  of 
a  fuse  shunting  the  trip  coil.  In  connection  with  this  arrange- 
ment, however,  it  is  to  be  noted  that  the  time  element  of  the 


FIG.  22. 


;8  Three-Phase  Transmission 

fuse  will  in  general  alter  with  its  current  carrying  capacity,  and 
accordingly  a  wide  range  of  current  transformers  with  various 
ratios  of  transformation  become  necessary  to  render  the  same 
type  of  fuse  suitable  for  different  circuits.  Moreover,  under  the 
conditions  of  short  circuits  the  time  element  of  fuses  disappears, 
and  it  is  difficult  to  ensure  that  discrimination  as  to  their 
succession  of  operation  with  two  or  more  of  such  devices  on 
the  same  circuit  shall  be  retained. 

As  a  modern  type  of  relay  we  may  select  a  well-known 
form  illustrated  by  Fig.  22,  made  by  Messrs  Ferranti.  This 
relay  consists  of  a  metal  disc  rotating  between  a  pair  of 
shaded  poles  energised  by  a  current  transformer  whose  primary 
winding  is  in  series  with  the  high-pressure  circuit  the  relay  is 
intended  to  protect.  The  torque  tending  to  rotate  the  pivoted 
disc  is  resisted  by  a  weight  suspended  by  a  thread  passing 
over  a  small  pulley  upon  the  spindle  of  the  disc.  Once  the 
current  through  the  magnet-winding  is  sufficient  to  overcome 
the  resisting  torque  due  to  the  suspended  weight,  this  is  raised, 
and  upon  reaching  its  highest  position  closes  the  trip  coil  circuit 
and  operates  the  oil  switch  in  series  with  the  E.H.P.  circuit. 

Calibration  curves    illustrating   the   action    of  this  type   of 

relay   are   shown    in    Fig.    23.     The   law  of  the   top  curve    is 

y^ 
approximately  T  =  -^+B,  where  T   is  the  time  taken   by  the 

relay  to  operate,  c  is  the  current  passing  through  the  magnet- 
winding,  and  A  and  B  are  constants.  The  retarding  effect  of 
the  copper  shoes  or  "  shading  "  upon  the  magnetism  emanating 
from  the  poles  is  to  transform  the  oscillating  field  which  would 
be  obtained  with  the  poles  unshaded  into  an  elliptically  rotating 
field,  having  a  period  of  revolution  identical  with  the  frequency 
of  the  magnetising  current  in  the  coils  of  the  magnet. 

We  know  that  the  velocity  of  a  rotating  field  in  the  case  of 

an  induction  motor  is  given  by  /,  where  /  is  the  frequency  of 

the  alternating  current,  and  P  is  the  number  of  pairs  of  poles 
in  any  one  phase. 

In  the  case  of  the  relay  under  consideration  we  have  an 
induction  motor  with  one  pair  of  poles.  The  speed  of  the 
rotating  field  is,  therefore,  equal  to  the  frequency  or /revolutions 
per  second.  It  would,  however,  be  oscillating  in  character,  and 
therefore  have  no  effective  torque  upon  the  disc  if  it  were  not 


Inverse  Time  Element 


79 


for  the  shaded  poles.     The  effect  of  the  copper  pole-pieces  is 
to  retard  the  magnetism  of  this  portion  of  the  pole-pieces,  so 


8  ?  8  8 

that  the  resultant  effect  is  that  of  a  tuft  of  magnetism  sweeping 
across  the  face  of  the  pole-pieces,  and  dragging  the  copper  disc 
with  it. 


8o 


Three-Phase  Transmission 


It  is  specially  to  be  noted  that  the  limiting  speed  which 
could  be  attained  by  the  disc  would  be  f  revolutions  per  second, 
less  the  slip  required  to  generate  sufficient  eddy  currents  in  the 
disc  to  overcome  the  retarding  forces  of  the  suspended  weight 
and  brake  magnet. 

Now  in  the  case  of  short  circuits  heavy  currents  will  pass 
through  the  relay  magnet.  A  powerful  torque  will  thus  be 
exerted  on  the  disc  momentarily,  and  it  will  immediately  speed 
up  to  reduce  the  slip.  How  quickly  and  nearly  the  disc 
approaches  synchronous  speed  will  depend  upon  the  extent  of 
the  short  circuit  current,  the  inertia  of  the  disc  and  the  retarding 
forces  of  the  weight  and  permanent  magnet. 


RELAY 


FIG.  24. 

Having  reviewed  the  function  of  the  relay  itself  it  becomes 
of  importance  to  note  some  special  features  in  the  grouping  of 
such  apparatus  upon  switchboards  usually  carried  out. 

It  may  be  readily  shown  that  complete  protection  will  only 
be  ensured  by  installing  a  separate  current  transformer  upon 
each  phase  in  circuit  with  a  separate  relay. 

The  arrangement  shown  in  Fig.  24  is  sometimes  adopted  ; 
two  current  transformers  only  cross  connected  being  employed 
in  combination  with  a  single  relay.  This  arrangement  possesses 
the  following  defects  : — 

If  the  neutral  points  of  the  generators  are  earthed  in   ac- 


Grouping  of  Relays  81 

cordance  with  the  usual  practice,  a  fault  to  earth  upon  the 
middle  phase  could  occur  without  affecting  the  current  trans- 
formers and  opening  the  automatic  switch. 

Moreover,  as  the  current  transformers  are  connected  up,  the 
current  which  must  operate  the  relay  is  the  vectorial  sum  of  the 
two  secondary  currents  cr  N/^  X  c  x/  if  the  current  in  the  secondary 
winding  of  each  transformer  \spxc  amperes  at  the  overload/ 
at  which  it  is  required  the  relay  shall  operate. 

If  now  an  overload  occur  between  one  of  the  phases  only  in 
which  there  is  a  current  transformer,  and  the  phase  in  which 
there  is  no  current  transformer,  a  much  greater  overload  must 
occur  before  the  relay  will  operate  ;  this  overload  current  being 
the  vectorial  resultant  of  c  and  ^xpc  drawn  as  to  their  correct 
phase  relationship. 

Further  difficulties  are  met  where  polyphase  relays  or  three- 
phase  magnets  actuating  the  same  armature  or  disc  are  em- 
ployed. In  this  instance  if  a  fault  occurs  between  one  phase  and 
earth,  upon  a  system  where  the  neutral  points  of  the  generators 
are  earthed,  a  much  larger  overload  on  this  one  phase  will 
generally  be  required  to  actuate  the  mechanism  than  if  the 
overload  occurred  simultaneously  on  all  three  phases. 

We  may  now  proceed  to  discuss  briefly  the  general  working 
conditions  to  be  met  by  time  element  apparatus  in  practice.  All 
of  the  devices  so  far  described  possess  an  inverse  time  element. 
That  is,  the  larger  the  overload  the  smaller  will  be  the  time 
taken  by  the  apparatus  to  act.  Some  clockwork  relays  have  been 
devised,  however,  to  allow  a  fixed  interval  to  elapse,  whatever 
be  the  magnitude  of  the  overload,  before  tripping  the  switch. 

This  feature  is  not  really  required,  but  an  inverse  time 
element  allowing  of  a  predetermined  sequence  of  operation  of 
automatic  switches  in  series.  For  instance,  with  feeder  switches 
it  is  of  importance  that  an  overload  should  cause  the  distant 
switches  to  operate  before  those  at  the  out-going  end  of  the 
feeder,  which  latter  should  have  a  time  lag  sufficient  to  ensure 
this  result.  With  relays  of  disc  type  this  means  that  the  number 
of  revolutions  made  by  the  discs  before  completing  the  trip  coil 
circuit  must  differ  on  the  home  and  distant  feeder  switches,  in 
other  words,  the  space  moved  through  by  the  contact  mechanism 
must  vary.  Under  the  extreme  conditions  of  a  short  circuit, 
however,  it  is  usually  difficult  to  ensure  discrimination  between 
more  than  three  relays  on  the  same  circuit. 
6 


82  Three-Phase  Transmission 

The  problem  of  adequate  protection  in  the  case  of  faults 
upon  the  system  is  further  complicated  where  substations 
contain  moving  machinery.  In  such  cases  synchronous  and 
induction  motors  will  often  feed  back  through  faults  necessi- 
tating the  use  of  what  are  known  as  reverse  relays  to  be 
described  later.  With  substations  containing  static  trans- 
formers and  induction  motors  the  outgoing  feeder  relays  are 
sometimes  set  to  operate  in  about  four  seconds,  whilst  the  distant 
relays  are  set  to  operate  in  two  seconds  or  less,  both  under  the 
conditions  of  short  circuit.  In  the  case  of  substations  containing 
synchronous  machinery,  however,  much  shorter  times  will  gener- 
ally be  necessary  to  prevent  the  synchronous  motors  falling  out 
of  step  when  a  short  circuit  occurs.  No  hard  and  fast  rules  can 
be  given  to  suit  all  cases,  and  the  time  element  setting  of  the 
relays  on  any  particular  system  should  be  determined  ex- 
perimentally to  suit  the  special  conditions  to  be  met. 

In  Fig.  23  calibration  curves  are  given  illustrating  the  time 
element  of  a  disc  relay.  As  a  practical  example,  take  the  case 
of  a  substation  containing  motor  generators  connected  by  a 
feeder  to  the  generating  station.  Suppose  at  the  generator 
end  of  the  feeder  a  time  element  relay  fixed,  also  a  number  of 
such  relays  in  the  substation.  A  short  circuit  on  one  of  the 
motor  generators  might  open  the  relay  switch  at  the  generator 
end  of  the  line  as  well  as  the  local  relay  on  the  faulty  machine. 

Suppose  the  feeder  carrying  60  amperes  and  at  the  sub- 
station supplying  three  branches  of  20  amperes,  each  branch 
having  its  own  relay,  and  each  relay  set  to  act  in  equal  times 
of  seven  seconds  at  50  per  cent,  overload.  The  feeder  relay  will 
act  at  90  amperes.  The  local  relay  will  act  at  30  amperes.  At 
full  load  the  main  feeder  carries  60  amperes.  At  full  load  the 
subfeeder  carries  20  amperes. 

Now,  a  fault  upon  any  one  motor  generator  causing  an 
increase  in  the  current  of  30  amperes,  or  250  per  cent,  overload, 
will  cause  the  local  relay  to  act  in  about  two  and  a  half  seconds 
whilst  the  feeder  relay  will  operate  in  seven  seconds. 

Suppose,  however,  that  a  short  circuit  occurs  increasing  the 
feeder  current  by  90  amperes,  or  250  per  cent,  overload.  The 
relay  would  operate  in  two  and  a  half  seconds  and  the  local 
relay  would  take  almost  the  same  time.  Therefore,  in  all 
probability  the  main  feeder  switch  will  be  brought  out  as  well 
as  the  local  cut  out. 


Reverse  Relays  83 

If  we  can  separate  the  horizontal  portion  of  the  curves  con- 
necting time  and  overload  with  the  two  sets  of  instruments  the 
less  likely  is  this  result  to  occur.  By  providing  a  greater  length 
of  cord  to  be  wound  up  by  the  feeder  relay  disc  than  by  the 
local  relay  disc  before  contact  is  made  closing  the  trip  coil 
circuit,  the  successive  operation  of  the  switches  in  the  desired 
order  may  be  ensured. 

Reverse  Relays. — We  now  come  to  the  consideration  of 
what  are  known  as  reverse  relays,  their  function  being  to  impart 
to  automatic  oil  switches  upon  alternating  current  circuits 
similar  features  to  those  possessed  by  polarised  direct  current 
circuit  breakers,  which  open  the  circuit  immediately  a  current 
flows  in  a  reverse  direction  to  that  required. 

Alternating  current  reverse  relays  may  be  classed  broadly 
under  two  headings  : — 

(a)  Reverse  Current  Relays. 
(£)  Reverse  Power  Relays. 

The  usual  positions  for  such  apparatus  upon  alternate  current 
systems  are  : — 

(1)  At  the  far   end    of  feeders  supplying  substations  con- 
taining moving  machinery  or  coupled   up  to  other  substation 
networks,  which  would  result  in  a  fault  upon  the  feeder  being 
fed  back  from  the  substation  itself,  causing  an   extensive  dis- 
organisation   of  the   supply  unless  the  local  feeder  switch  be 
opened  immediately. 

(2)  Between  each  generator  and  the  main  bus  bars,  to  ensure 
that  a  faulty  generator  be  at  once  disconnected  from  the  bus 
bars  and  interference  with  other  healthy  generators  be  obviated. 

Reverse  Current  Relays. — As  an  interesting  example  of  a 
reverse  current  relay,  many  of  which  might  be  quoted,  may 
be  mentioned  an  ingenious  arrangement  devised  by  Andrews. 
This  consists  of  a  differentially  wound  solenoid  acting  upon  an 
iron  core,  which,  when  lifted,  closes  the  trip  coil  circuit.  The 
two  windings  of  the  solenoid  are  connected  in  parallel  across 
the  secondary  of  a  transformer  at  low  pressure,  and  traverse 
also  what  is  called  an  "  equaliser,"  upon  which  is  wound  one 
turn  of  the  main  circuit  to  be  controlled  (Fig.  25).  If  no  current 
flows  in  the  main  circuit,  the  low-pressure  current  divides  equally 
between  the  differential  windings  of  the  solenoid  and  has  no 


Three-Phase  Transmission 


effect  upon  the  iron  core.  Should,  however,  the  phase  displace- 
ment of  the  current  in  the  main  winding  be  such  as  would  result 
from  a  fault,  the  balance  of  the  currents  in  the  differential 

CO 


1 


windings  will  be  upset,  resulting  in  the  core  being  raised,  thus 
completing  the  trip  coil  circuit. 

Reverse    Power    Relays.— The   most   important   of  these 


Wattmeter  Type  Relay 


devices  involve  the  adoption   of  the  wattmeter  principle  to  a 
relay  originally  suggested    by  Professor    Sylvanus  Thompson. 


FIG.  26. 

Reverse  Power  Relay  Connections. 

BUS    BAR 


BUS    BAR 


P.T.F 


M.S.  =  Main  Switch. 
T.C.=  Trip  Coil. 
R.S.C.  =  Relay  Shunt  Coil. 
R.M.C.  =  Relay  Main  Coil. 

Q.  =  Generator. 
C.T.  =  Current  Transformer. 


R.M  C. 


P.T.  =  Potential  Transformer. 
P.  T.  P.  =  Potential  Transformer  Fuse. 
B.C.  --Relay  Contactor. 

B-  =  Battery    or    other     source     of 

E.M.F.  for  operating  T.C. 
LI_i.  —Indicating  Lamp. 


FIG.  27. 


When  the  phase  difference  of  voltage  and  current  are  such  as 
to  result  in  the  flow  of  energy  in  the  reverse  direction  in  an 
alternating  current  feeder,  the  relay  closes  the  trip  coil  circuit. 


86 


Three-Phase  Transmission 


A  compact  form  of  this  apparatus  is  made  by  Messrs  Ferranti, 
and  is  illustrated  by  Figs.  26  and  27. 

Fig.  26  explains  the  manner  in  which  the  wattmeter  disc, 
whilst  held  by  a  catch  T  from  rotating  in  a  clockwise  direction, 
is  free  to  rotate  in  a  counter  clockwise  direction,  and  in  doing 
so  will  close  the  trip  coil  circuit. 

One  point  to  be  carefully  borne  in  mind  with  the  use  of 
this  type  of  apparatus,  depending  as  it  does  upon  a  potential 
transformer,  is  that  under  the  conditions  of  a  short  circuit  the 
potential  difference  between  the  bus  bars  whether  at  the  sending 
or  receiving  end  of  the  line  may  be  so  reduced  that  the  apparatus 
may  fail  to  act. 

It  is  further  evident  that  since  the  operation  of  this  type  of 

T,  T2 


*J^S\S\J\S^ 


FIG.  28. 

relay  requires  a  certain  number  of  watts  or  real  power  in  the 
circuit,  any  reduction  in  pressure  means  that  an  increased  current 
will  be  necessary.  Similarly  if  the  power  factor  of  the  circuit 
be  low,  although  the  pressure  may  be  maintained,  an  increased 
current  will  again  be  necessary  to  operate  the  relay.  From 
the  preceding  remarks  it  will  be  gathered  that  to  prevent  the 
reverse  current  assuming  dangerous  proportions  before  the 
relay  operates,  it  is  necessary  to  strictly  limit  the  reverse  power 
setting.  This  in  the  case  of  relays  protecting  generators  is 
sometimes  made  as  low  as  10  per  cent,  of  the  generator  output ; 
the  power  factor  of  motoring  currents  being  generally  low  in 
the  case  of  relays  protecting  feeders,  the  reverse  power  setting 
may  be  20  per  cent,  or  more  of  the  full-rated  load  of  the  feeder ; 


Merz-Price  Gear 


FIG.  29. 


88 


Three-Phase  Transmission 


the  power  factor  of  a  fault  current  will  in  this  case  generally  be 
high.     It  is  obvious  that  if  the  reverse  setting  be  made  too  low 

the  hunting  of  substation 
machinery  or  synchronising 
currents  of  the  generators 
may  open  the  switches  when 
this  is  unnecessary.  Gene- 
rally speaking  a  time  ele- 
ment with  reverse  power 
relays  is  undesirable,  and 
when  a  fault  occurs  the 
more  quickly  it  can  be  iso- 
lated from  the  system  the 
better,  and  the  less  likely 
is  the  pressure  to  have 
fallen  to  such  an  extent 
as  to  render  the  relay  in- 
operative. 

As  regards  the  grouping 
of  reverse  power  relays  the 
same  considerations  hold 
as  in  the  case  of  maximum 
time  limit  relays,  and  com- 
plete protection  can  only 
be  ensured  by  employ- 
ing an  independent  relay 
and  transformer  for  each 
phase. 

Merz-Price  Protective 
Gear.  —  No  description  of 
protective  switch  gear  would 
be  complete  without  some 
reference  to  the  Merz-Price 
system,  which  is  extensively 
used  by  the  Newcastle  and 
Durham  Power  Companies 
FIG.  30.  to  protect  some  hundreds  of 

miles  of  extra  high-pressure 

cable  in  networks  including  feeders,  interconnectors,  and  branch 

circuits. 


Merz-Price  Gear 


89 


The  essential  points  claimed  for  this  apparatus  are — 
(a)  The  switches  do  not  act  in  the  case  of  surging  or  tem- 
porary overload. 

(V)  The  switches  only  act  when  an  actual  defect  arises,  and 
then  only  on  the  defective  section. 

The  principle  of  this  protective  device  will  be  grasped  at 
once  upon  reference  to  Figs.  28  and  29. 

Small  current  transformers,  Tx,  T2,  are  placed  at  each  end  of 
the  line  with  their  primary 
windings  in  series  with  it,  and 
the  secondary  windings  are 
likewise  connected  in  series 
with  one  another,  and  with 
relays  Rx  and  R2,  for  actuating 
automatic  switches  by  means 
of  a  small  auxiliary  cable. 

As  the  secondary  windings 
are  opposed  to  one  another  it 
will  be  seen  that  balance  exists 
for  all  loads,  and  that  only  in 
the  case  of  a  fault  on  the 
feeder  will  a  current  flow  in 
the  relay  circuit  which  will 
then  open  the  switches  at  each 
end  of  the  line  simultaneously. 

The  type  of  relay  used  with 
this  gear  is  illustrated  by  Fig. 
30,  and  a  current  transformer 
of  ring  type  suitable  for  a 
20,000  volt  circuit  is  illustrated 
by  Fig.  31.  FIG.  31. 

The   same    principle    is 

adopted    to    protect   three-phase   cables    in    parallel,   banks   of 
transformers,  &c. 

In  applying  this  system  of  protection  to  three-phase  cables, 
a  three-core  pilot  cable  is  laid  with  each  feeder  to  form  the 
subsidiary  relay  circuits,  which  it  is  of  importance  should  be 
insulated  from  earth  to  avoid  the  tripping  of  the  switches  on 
healthy  feeders  from  earth  currents  set  up  by  a  fault. 

As  one  example  of  the  practical  utility  of  this  apparatus 
may  be  cited  that  of  an  interconnector  between  two  substations. 


90  Three-Phase  Transmission 

The  Merz-Price  gear  will  allow  of  the  flow  of  energy  in  either 
direction  between  the  substations,  but  upon  a  fault  occurring 
upon  the  interconnector  itself  it  is  instantaneously  cut  out  of 
circuit.  It  is  obvious  that  independent  reverse  relays  could  not 
be  employed  under  such  conditions,  and  that  maximum  relays 
at  the  ends  of  the  interconnector,  set  high  enough  to  allow  of 
temporary  surges  of  power,  could  not  be  arranged  to  isolate  the 
interconnector  instantaneously  and  before  a  fault  current  had 
reached  dangerous  proportions,  as  would  be  the  case  with  the 
Merz-Price  gear  in  use. 

It  is  to  be  noted,  however,  in  connection  with  this  protective 
gear,  that  the  feeder  cables  are  not  protected  against  ordinary 
overload  such  as  might  be  occasioned  by  the  failure  of  an  oil 
switch  in  a  substation  ;  its  application  to  an  existing  system  of 
feeder  cables  also  would  be  expensive  in  most  cases  unless  suit- 
able pilot  wires  were  available. 


CHAPTER    V. 
IMPEDANCE,    PRESSURE   RISE,    HARMONICS,   &c. 

WE  have  already  seen  under  Chapter  II.,  Lead  Sheath  Losses, 
that  the  impedance  of  a  three-phase,  lead-covered,  paper- 
insulated  cable  is  increased  by  the  type  of  armouring  or  trough- 
ing  by  which  it  is  surrounded,  whereas  it  is  diminished  by  the 
effect  of  the  secondary  currents  induced  in  the  lead  sheath.  In 
considering  the  effect  of  impedance  in  a  three-core  cable  it  is 
convenient  to  deal  with  one  core  only.  This  may  to  some 
engineers  at  first  sight  present  some  difficulty  from  the  fact  that 
if  we  assume  a  single  conductor  carrying  current  and  try  to 
calculate  its  self-induction  from  the  number  of  lines  of  force 
surrounding  it  when  removed  from  all  other  conductors,  we 
arrive  at  a  value  infinity.  The  reason  is,  there  must  always  be 
a  return  conductor  somewhere,  and  we  will  define  the  self- 
induction  of  one  core  of  the  cable  as  half  that  of  the  self- 
induction  of  two  cores,  one  acting  as  flow  and  the  other  as 
return  ;  this  will  vary  directly  as  the  distance  apart  of  the  two 
cores  and  as  the  sectional  areas  of  the  cores  themselves.  Now, 
with  a  three-phase  cable  having  cores  symmetrically  spaced,  the 
currents  under  three-phase  working  conditions  are  displaced  by 
a  phase  difference  of  120° ;  thus,  although  when  using  two  cores 
only  of  the  cable  as  flow  and  return  half,  the  E.M.F.  of  self- 
induction  so  measured  will  give  the  value  per  core  ;  yet  when 
working  three-phase  the  E.M.F.  of  self-induction  measured 
between  phases  must  be  divided  by  \/3  to  arrive  at  the  E.M.F. 
of  self-induction  per  core. 

The  test  figures  given  by  Table  XVIII.  will  illustrate  this 
point. 


Three-Phase  Transmission 


TABLE  XVIII.— TEST  OF  IMPEDANCE  OF  6.2  MILES  OF 
(THREE-CORE  0.15  SQ.  IN.)  EXTRA  HIGH-TENSION 
FEEDER  AT  50  ~. 


P.  D.  between  Phases  at  Sending  End 
in  Volts. 

Current  per  Core  at  Sending 
End  in  Amps. 

Impedance 
per  Single 

Mean 

Ohms. 

V, 

V9 

Mean. 

~vT 

Cl 

C,            Mean. 

89 

88.5 

88 

51.2 

26 

25              25.5 

2.01 

90 

90.5 

90.5 

52.2 

26 

25.5           25.75 

2.03 

99 

99 

99-5 

57.2 

28.5 

28              28.25 

2.O2 

1  08 

1  08 

1  08 

62.5 

31-5 

31              31.25 

2 

116.5 

116 

116.5 

67.2 

34 

33-5         33-75 

1.99 

119 

119 

118.5 

68.6 

34-2 

34            34-  1 

2.01 

Mean    =    2.01 

One  phase  was  disconnected  and  the  following  readings  were 
taken  : — 


P.  D.  between  Phases  at 
Sending  End  in  Volts. 

Current  per  Core  at  Sending  End 
in  Amps. 

Impedance 
per  Single 

\\-\, 

V 

2 

c, 

c. 

Mean. 

Ohms. 

92 

46 

22.5 

22 

22.25 

2.07 

100 

5° 

25 

24 

24.5 

2.04 

99-5 

49-75 

25.5 

24 

24.7 

2.O2 

110.5 

55-25 

27-5 

26.5 

27 

2.04 

122 

61 

31.2 

30.5 

30.8 

I.98 

123-5 

61.75 

31-5 

30-7 

3I-I 

1.99 

140 

70 

35-7 

34-5 

35-i 

2 

141 

70.5 

35-8 

35 

35-4 

1.99 

Mean  "             2.01 

It  is  useful  at  this  point  to  note  the  following  items  :— 
Resistance  due  to  self-induction  =  27r«L=/L  ohms, 
E.M.F.  due  to  self-induction       =  27mLC  =/LC  volts, 
where  n  =  frequency. 

L  =  self-induction  in  henrys  per  conductor. 
R  =  resistance  in  ohms  per  conductor. 
f=  current  in  amperes  per  conductor. 
Impedance  of  conductor  =  Resultant  ohms=  \/R2  +/2L2. 


Induction  of  Paper  Cables 


93 


In  the  case  of  low-pressure  distributors  of  three  and  four 
core  type,  the  impedance  may  often  become  of  importance  by 

Induction  per  Core  per  Mile  at  50  ~  of  Paper-Insulated 

E.S.C.  Three-Core  Cables  Constructed  for  Various 

Working  Pressures. 

Z6 


•24 


•22 


•20 


-16 


•12 


'o 


05  0-1  -15  -2  25 

Section  per  Core  in  Square  Inch. 

FIG.  32. 

increasing   the   drop    in    pressure   over   that  due   to   resistance 
alone  by  as  much  as  20  per  cent,  or  more.     With  high-pressure 


94  Three-Phase  Transmission 

cables,  although  this  impedance  may  exceed  the  copper  resist- 
ance by  as  much  as  40  to  50  per  cent.,  the  drop  in  pressure  will 
in  general  be  but  a  small  percentage  of  the  transmission  pressure, 
and,  therefore,  of  little  importance. 

In  Figs.  32  and  33  curves  are  given  illustrating  the  induc- 
tion effect  per  core  of  paper  cables  constructed  according  to  the 
Engineering  Standards  Committee's  specification  as  regards 
thickness  of  dielectric,  &c.,  for  the  working  pressures  stated. 

It  is  interesting  to  note  that  with  a  working  pressure  of 


e 

9 

0  30% 

E. 

9 

Q. 


O'l  O-15  O2. 

Section  pen  Core  in  Square  Inch. 

FIG.  33- 


015 


20,000  volts  the  impedance  per  core  of  a  0.25  sq.  in.  three-core 
cable  exceeds  the  copper  resistance  by  nearly  40  per  cent. 

In  the  case  of  four-core  cables  used  for  three-phase  working, 
one  of  the  conductors,  usually  termed  the  neutral,  will  carry  the 
out-of-balance  current  only.  The  presence  of  this  fourth  or 
neutral  conductor  disturbs  the  symmetrical  spacing  of  the  live 
conductors  since  one  of  these  will  have  an  active  conductor 
upon  each  side  of  it,  whereas  the  two  remaining  live  conductors 
will  have  an  active  conductor  on  one  side  of  them  only.  The 


Impedance  of  Four-Core  Cables 


95 


following  test  on  a  drum  containing  220  yards  of  0.15  sq.  in. 
L.T.  four-core  British  Insulated  &  Helsby  Cable  Co.'s  lead- 
covered  cable  will  illustrate  this  point. 

Star  connected  transformers  were  joined  to  one  end  of  the 
cable,  and  at  the  other  end  three  coils  of  /„  V.I.R.  cable 
(braided  only)  were  joined  in  star. 

Each  of  the  three  conductors  was  joined  consecutively  to 
an  oscillograph  to  record  the  current  flowing  in  it,  and  the  drop 
in  pressure  along  the  conductor. 

The  results  obtained  are  given  in  Table  XIX. 


TABLE  XIX. 


Core  of  Cable. 

Red. 

Blue. 

Green. 

Neutral. 

(i)  Amperes 

12.5 

11.50 

11.90 

0.00 

P.D.  along  conductor 

.568 

.460 

.625 

... 

Impedance  —  —   - 

.045 

.040 

.052 

y 

Direct  current  — 

.0387 

.0388 

.0386 

(2)  Amperes 

13-6 

9.87 

12.27 

5.0 

P.D.  along  conductor           -          .642 

.384 

.568 

y 

Impedance  =  —   - 

.047 

.0389 

.0477 

Direct  current  -^ 

.0387 

.0388 

.0386 

From  the  above  table  it  will  be  seen  that  the  impedance 
for  the  blue  conductor,  which  has  an  active  conductor  on  each 
side  of  it,  is  small,  whereas  the  red  and  green  conductors, 
which  have  an  active  conductor  on  one  side  only,  have  an 
impedance  of  about  20  per  cent,  in  excess  of  that  with  direct 
current.  The  current  in  the  red  and  green  conductors  had  a 
considerable  lag,  whereas  that  in  the  blue  conductor  had  but  a 
small  lag. 


96  Three-Phase  Transmission 

Pressure  Rises. 

The  principal  causes  of  pressure  rise  met  with  in  trans- 
mission circuits  may  be  classed  as  follows  : — 

(1)  Resonance. 

(2)  Power  surges. 

(3)  Reflected  waves. 

(4)  Concentration  of  potential. 

(5)  The   effect   of  leading    currents  on   generators   and 

transformers. 
In  what  follows  it  is  proposed  to  discuss  briefly  these  effects. 

Resonance. — In  acoustics  we  have  very  familiar  cases  of 
resonance.  As  examples,  a  great  number  of  which  might  be 
mentioned,  we  may  note  the  singing  of  violin  strings  when 
in  the  neighbourhood  of  a  piano  upon  which  notes  are  struck 
in  sympathy  with  the  period  of  vibration  of  the  string ;  the 
same  effect  occurs  with  gas  globes  or  other  objects  in  a  room  in 
which  musical  sounds  are  being  produced.  This  phenomenon 
of  resonance,  which  we  find  present  in  all  the  principal  sciences, 
is  very  much  in  evidence  in  alternating  current  circuits.  To  take 
a  mechanical  analogy,  we  may  suppose  a  heavy  weight  w 
attached  to  a  spiral  spring  which  we  know  will  possess  a 
natural  frequency  of  vibration  and  which  we  may  denote  by 
the  letter  n.  If  we  now  impart  to  the  point  of  support  a  forced 
vibration  of  frequency  m  it  may  be  readily  shown  that  the 
amplitude  of  the  vibration  A  of  the  weight  w  will  be  : — 

A  =  -    - — -  times  that  of  the  point  of  support. 


If  n  equal  m  we  have  an  amplitude  theoretically  infinity. 

It  is  of  great  importance  to  notice  from  the  above  formula 
that  when  the  motion  of  the  point  of  support  is  a  small  fraction 
of  the  natural  frequency,  the  forced  vibration  of  the  weight  is 
practically  a  copy  of  the  motion  of  the  point  of  support ;  in 
other  words,  the  spring  and  weight  w  move  like  a  rigid  body, 
but  as  the  frequency  of  the  forced  vibration  gets  more  nearly 
equal  to  the  natural  frequency  of  vibration  of  the  weight  on  the 
spring  the  amplitude  of  its  motion  is  enormously  increased.  It 
will  also  be  noticed  that  when  the  forced  vibration  is  made 
many  times  the  frequency  of  the  natural  vibration  of  u>,  the 


Resonance 


97 


amplitude  of  w  becomes  less  and  less.  This  result  we  know 
by  experience  to  be  the  case.  An  interesting  piece  of  apparatus 
based  upon  this  fundamental  principle  has  been  developed  for 
determining  the  frequency  of  an  alternating  current.  The 
construction  of  this  apparatus  is  shown  in  Figs.  34  and  35, 
and  is  known  as  Frahm's  frequency  indicator.  As  will  be 
seen,  it  consists  of  a  number  of  vibrating  tongues,  such  as  we 
find  in  an  ordinary  musical  box,  each  of  which  is  weighted 
and  of  sufficient  length  to  have  a  natural  frequency  of  vibration 
to  correspond  with  the  natural  frequencies  of  those  alternating 
current  circuits  usually  to  be  met  with  in  practice.  The  alter- 
nating current  whose  frequency  is  to  be  determined  causes  the 
point  of  support  of  these  tongues  to  vibrate  by  means  of  an 
electro-magnet  through  which  the  alternating  current  passes, 


FIG.  34. 


FIG.  35. 


when  one  or  more  of  the  tongues  will  be  set  in  violent  oscilla- 
tion, according  as  its  natural  frequency  of  vibration  is  in 
sympathy  with  that  of  the  point  of  support. 

It  is  shown  in  text-books  that  if  we  have  a  circuit  consisting 
of  a  self-induction  of  L  henrys  in  series  with  a  capacity  of  K 
farads,  as  in  Fig.  36,  the  circuit  will  possess  a  natural  frequency 
for  electrical  oscillations  ;  this  frequency,  N,  being  given  by  the 
expression  :  — 


If  in  this  circuit  be  included  an  alternator  of  voltage  V  and 
frequency  N,  we  have  the  conditions  necessary  for  electrical 
resonance  and  the  amplitude  of  the  current  C  will  become  very 
large,  depending  only  upon  the  ohmic  resistance  of  the  con- 
ductors -and  alternator  ACB  in  Fig.  36. 
7 


98  Three-Phase  Transmission 

The  necessary  conditions  for  resonance  may  be  stated  in 
another  way.  If  the  self-induction  L  be  alone  in  circuit,  the 
current  Q.  would  be 


Similarly,  if  the  condenser  were  alone  in  circuit  the  current 

CK  would  be 

CK  =  27rNKV  amperes  (3) 

When    CL  =  CK    we    have    the  necessary   condition  for   re- 
sonance, for  equating  (2)  and  (3)  we  get 

<~N).-JL,  or  N-^/JL  as  before. 


We  know  also  that  for  any  current  C  traversing  the  circuit 
the  pressure  across  the  self-induction  will  lag  90°  behind  this 
current,  whilst  the  pressure  across  the  condenser  will  be  90 
in  advance  of  this  current.  These  two  pressures  will  be  thus 
equal  and  opposite  at  every  instant.  Hence,  when  resonance 
occurs  the  effect  is  the  same  as  if  AB  were  short-circuited. 
The  current  C  is  then  only  limited  by  the  resistance  of  the 
circuit  ACB. 

If  C1  =  self-induction  current  or  condenser  current  when  one  or  the 

other  is  alone  in  circuit. 
p 
— j  V  =  pressure  across  AD  or  D  B,  and  this  may  reach  a  highly 

destructive  value. 
The  rise  of  potential  within  the  circuit  being  given  by  C*  /  ^. 

*         JK. 


Resonance  with  Harmonics  99 

It  is  to  be  noted  at  this  point  that  harmonics  present  upon 
the  fundamental  pressure  wave  are  in  general  quite  free  to  act 
as  separate  entities  in  producing  resonance.  In  fact  with  serious 
resonance  of  harmonics  the  fundamental  wave  may  become 
almost  indistinguishable,  being  replaced  by  a  wave  of  great 
amplitude  with  a  frequency  as  many  times  that  of  the  funda- 
mental as  corresponds  to  the  order  of  the  particular  harmonic 
for  the  resonance  of  .which  the  conditions  of  the  circuit  are 
favourable.  Let  us  take  a  particular  case.  A  star  wound  500- 
kw.  5,ooo-volt  three-phase  generator  was  found  to  have  an 
average  impedance,  due  to  self-induction,  of  34.5  ohms  per 
phase  at  a  frequency  of  50  cycles,  corresponding  to  a  short 
circuit  current  of  145  amperes  at  5,000  volts  ;  10  miles  of  three- 
core  0.15  sq.  in.  5000- volt  cable  will  take  a  minimum  charging 
current  of  2.96  amperes  per  phase. 

Now  suppose  a  strong  7th  harmonic  present  in  the  pres- 
sure wave  of  the  alternator.  The  charging  current  due  to  this 
harmonic  will  increase,  whereas  the  current  through  the  self- 
induction  will  diminish,  in  proportion  to  the  frequency.  The 
short-circuit  current  through  the  alternator,  assuming  constant 

self-induction,  will  be  -     =  20.7  amperes.     The  charging  current 

in  the  cable  will  be  2.96x7  =  20.7  amperes.  It  will,  therefore, 
be  seen  that  we  have  the  necessary  condition  for  resonance  of 
the  7th  harmonic. 

Variations  in  the  forms  of  pressure  waves  due  to  conditions 
such  as  the  above  are  discussed  later  when  dealing  with  wave 
forms. 

It  is  to  be  noted,  however,  with  regard  to  triple  frequency 
harmonic  currents  and  multiples  that  the  generator  impedance 
to  these  will  not  be  three,  or  multiples  of  three,  times  that  due 
to  the  fundamental  wave,  for  the  reason  that  the  phase  relation- 
ship of  these  currents  in  the  windings  of  the  alternator  will 
produce  opposite  magnetising  effects  upon  the  iron,  and  thus 
the  impedance  to  these  higher  harmonic  currents  will  not  be 
strictly  proportional  to  their  frequency.  In  general  a  capacity 
considerably  in  excess  of  that  theoretically  necessary,  as  deter- 
mined by  the  above  considerations,  is  required  to  produce  exact 
resonance,  a  further  error  is  also  introduced  by  assuming  that  the 
self-induction  of  the  alternator,  as  deduced  from  the  value  of  its 
short-circuit  current  or  synchronous  impedance,  will  be  the  same 


IOO 


Three-Phase  Transmission 


for  all  loads  and  currents.  This  will  be  obvious  upon  consider- 
ing the  shape  of  the  synchronous  impedance  curves  of  most 
generators. 

It  may  be  gathered  from  what  has  preceded  that  resonance 
at  fundamental  frequency  will  not  generally  occur  with  com- 
mercial alternators  and  such  cable  systems  as  are  usually  fed  by 
same,  owing  to  the  fact  that  the  self-induction  of  the  alternator 
is  generally  too  small,  and  that  this  is  further  diminished  in 
proportion  to  the  number  of  similar  alternators  running  in 
parallel. 

*E 

SUB  STATION 


FIG.  37. 

Certain  conditions  may  arise,  however,  in  practice  which  will 
result  in  resonance  at  the  fundamental  frequency  of  the  system. 

As  an  example  we  may  take  the  case  of  a  substation  con- 
taining three  100  kw.  delta  connected  transformers  fed  by  a 
0.4  sq.  in.  three-core  cable  at  5,000  volts,  50  cycles,  from  a 
distributing  centre  one  mile  distant. 

The  magnetising  current  of  each  transformer  may  be  taken 
at  0.183  ampere,  corresponding  to  a  primary  impedance  of 
27,320  ohms  or  a  self-induction  of  87  henrys. 

The  core  capacities  of  the  cable  may  be  taken  as  follows  : — 

One  core  versus  two  others  bunched  to  lead  sheath  =  .26  microfarad. 
Three  cores  versus  lead,  sheath -0.5  microfarad. 


Resonance  at  Fundamental  Frequency     101 

Now,  consider  the  state  of  things  illustrated  by  Figs.  37 
and  38,  where  one  phase  is  shown  open  at  the  distributing 
station  and  another  phase  open  at  the  substation,  a  condition 
which  might  be  brought  about  by  the  blowing  of  fuses  F  Fj  upon 
an  overload  or  other  cause. 

Current  will  pass  from  the  generator  via  core  No.  3  of  the 
cable  to  the  transformer  terminal  3',  then  via  transformer  wind- 
ing 3'-2'  and  also  via  windings  3'-!'  in  series  with  i'-2'  to  core 
No.  2  of  the  cable.  From  core  No.  2  this  current  will  pass 


FIG.  38. 


through  the  condenser  formed  by  the  dielectric  between  cores 
2  and  i,  and  via  core  No.  I  back  to  the  generator. 

The  capacities  between  the  cores  of  the  cable  and  between 
cores  and  lead  sheath  are  equivalent  to  equal  condensers  K  and 
S  arranged  as  shown  in  Fig.  38. 

The  capacity  between  one  core  and  two  others  bunched 
to  the  lead  sheath  is  obviously  2  K  +  S,  whilst  the  capacity 
between  all  three  cores  bunched  together  and  the  lead  sheath 
is  3  S'. 


IO2 


Three-Phase  Transmission 


From  the  data  already  given,  therefore,  we  have 
2K  +  S  =  o.26  microfarad. 

3s  =  °-5 

from  \s'hich  we  deduce  K=    -045         ,, 

and  S  =  o.  1 7          „ 

Now  the  combined  self-induction  of  two  transformer  windings 
in  series  shunted  by  a  third  transformer  winding,  each  winding 
having  a  self-induction  of  87  henrys,  is  obviously  r!x87  =  58 
henrys.  Our  circuit,  therefore,  resolves  itself  into  reactive 
branches  consisting  of  a  self-induction  of  58  henrys  shunted 
by  a  capacity  of  .045  microfarad,  this  combination  being  in 
series  with  a  capacity  of  0.13  microfarad  (Fig.  39). 


0  13 


K=    04-5 


L=56 


FIG.  39. 

The  reactance  of  the  condenser  and  self-induction  in  parallel 
will  be : — 

_L        m        ^8 _       hen 

i  -/-LK.     i  -  (314)-  x  58  x  .045  x  io~° 

which  may  be  considered   as   in   series  with  the  condenser  of 
0.13  microfarad. 

But  the  condition  for  resonance  is  that  K  shall  be  equal  to 

_L,  orK  =          '          -ai3 
/-L'  (314)2x78      10"  ' 

We  see,  therefore,  that  the  necessary  condition  for  resonance 
is  satisfied  in  this  instance  at  the  fundamental  frequency  of  the 
circuit,  and  highly  destructive  pressure  rises  have  been  found 
to  occur  under  the  conditions  set  out  above. 

Power  Surges. — The  most  important  rises  of  pressure  upon 
transmission  lines  are  usually  those  due  to  power  surges,  such 
as  are  obtained  when  a  short  circuit  occurs  upon  the  line,  largely 


Power  Surges  103 

increasing  the  current,  which  is  subsequently  interrupted.  The 
surge  pressure  in  such  cases  has  been  found  to  depend  almost 
entirely  upon  the  magnitude  of  the  current  flowing,  and  to  be 
independent  of  the  length  of  the  line  and  its  working  pressure. 

If  we  have  a  circuit  made  up  of  a  large  condenser  K  (Fig.  40) 
in  series  with  a  self-induction  L,  and  suppose  the  condenser  to 
be  charged  to  a  high  potential,  we  know  that  on  closing  the 
switch  s  the  condenser  will  discharge  itself  through  the  self- 
induction,  the  current  increasing  until  the  condenser  is  fully 
discharged.  At  this  instant  the  whole  of  the  potential  energy 
stored  in  the  condenser  is  now  stored  in  the  self-induction  in 
the  form  of  electro-magnetic  energy.  The  current  will  not 
cease  to  flow  abruptly,  but  will  continue  in  the  same  direction 
due  to  the  E.M.F.  of  the  self-induction  until  the  condenser  is 


K 


s 

FIG.  40. 

again  charged,  but  with  reversed  polarity  to  that  originally. 
The  condenser  again  discharges  into  the  self-induction,  and 
the  current  oscillates  until  the  energy  of  the  charge  is  used  up 
in  the  heating  of  the  circuit. 

The  energy  stored  up  by  a  condenser  of  K  farads  charged 
to  a  potential  of  V  volts  in  watt-seconds  is  given  by  the  expres- 
sion |KV2.  Again,  the  energy  stored  up  in  the  magnetic  field 
of  a  self-induction  of  L  henrys,  when  carrying  a  current  of 
C  amperes  in  watt-seconds,  is  given  by  the  expression  |LC2, 
and  this  same  amount  of  energy  may  appear  alternately  as 
potential  or  electro-magnetic  in  a  precisely  similar  manner  to 
the  energy  of  the  bob  of  a  swinging  pendulum,  which  is  wholly 
potential  at  the  end  of  its  swing,  and  wholly  kinetic  as  it  passes 
the  lowest  point  of  its  swing. 

In  the  case  of  long  transmission  lines;  or  extensive  networks 


104  Three-Phase  Transmission 

of  extra  high-pressure  cables,  we  have  considerable  capacity 
and  self-induction,  and  when  such  circuits  are  carrying  heavy 
currents  at  the  instant  they  are  interrupted,  the  total  energy 
stored  electro-magnetically  in  the  field  surrounding  the  con- 
ductors of  the  circuit  will  appear  as  potential  energy,  charging 
up  the  circuit  to  a  very  high  voltage. 

Taking  as  an  example  the  case  of  an  overhead  transmission 
line,  we  may  assume  the  self-induction  L  of  one  line  wire  per 
mile  to  be  .0037  henry,  and  its  capacity  0.8  x  io~8  farad.  If 
a  short  circuit  occurred,  causing  the  interruption  of  the  line 
when  the  current  had  an  instantaneous  value  of  150  amperes, 
we  get  for  the  value  of  -^-LC2  the  electro-magnetic  energy  of  the 
circuit  :  — 

.0037  x  (150)'  watt-seconds. 

2 

Now  upon  the  interruption  of  the  line  this  energy  must 
appear  as  a  charge  increasing  the  potential  of  the  circuit  ;  in 
other  words 


V 


4  X  2  X  IO° 


=  103,000  volts. 

Experiments  made  in  America  upon  a  line  100  miles  in 
length,  short  circuited  at  the  far  end,  resulted  in  a  power  surge 
which  jumped  spark  gaps  4^  in.  in  width  at  the  generator  end 
of  the  line.  Allowing  24  kilovolts  as  an  ordinary  value  of  the 
dielectric  strength  of  air,  this  sparking  distance  would  in  itself 
correspond  with  an  instantaneous  pressure  rise  of  108,000  volts. 

It  will  be  found  that  in  cable  systems  the  pressure  rises 
are  not  anything  like  so  great  under  the  same  conditions.  For 
instance,  in  the  case  of  a  2O,ooo-volt  .05  sq.  in.  three-core  cable 
we  may  take  L  =  .748xio~3  henry  per  mile,  K  =  .2iixio~° 
farad  per  mile,  and  assuming  the  current  interrupted  to  have 
an  instantaneous  value  of  150  amperes  as  before,  we  get  — 


2  X  I03 


and  V  =  N4aI°  =  8,940  volts. 

In  practice  power  surges  are  very  much  more  complicated 
than  might  be  assumed  from  the  above  theoretical  considera- 


Power  Surges  105 

tions,  and  in  general  the  voltage  rise  due  to  a  surge  will  be 
superposed  upon  the  working  pressure  of  the  line. 

It  will  thus  be  seen  that  a  line  working  at  a  very  high 
pressure,  but  with  a  small  current,  may  not  be  subjected  to  so 
high  a  surge  pressure  as  a  line  at  lower  working  pressure  but 
having  a  much  larger  line  current. 

When  a  transmission  line  is  interrupted,  it  may  be  shown 
that  a  pressure  oscillation  will  be  started  of  maximum  value  V, 
which  will  be  slightly  less  than  that  given  by  the  expression  : — 


Where  Vl  =  instantaneous  value  of  line  pressure  at  time  of  interruption. 
C:  =  instantaneous  value  of  line  current  at  time  of  interruption. 
L  =  self-induction  per  mile  per  conductor  in  henrys. 
K  =  capacity  per  mile  per  conductor  in  farads. 

Take  the  following  examples  :  — 

LINE  PRESSURE                LINE 

PRESSURE.  TO  EARTH.  CURRENT. 

Volts.  Volts.  Amperes. 

(a)  60,000  48,000         50 

(b)  30,000  28,000        100 

And  values  of  L  and  K  :  — 

L  =  .ooig7  henry  per  mile. 
K  =  .oi53  microfarad  per  mile. 

If  we  assume  that  the  current  is  doubled  by  a  short  circuit 
at  the  time  of  the  line  being  interrupted,  and  that  the  instan- 
taneous value  of  the  line  pressure  is  equal  to  the  effective 
pressure,  then  we  get  for  the  first  case  :  — 

Va  =  >/(48ooo)2  +  1  288  x  io6  =  60,000  volts  ; 
and  for  the  second  case  :  — 


io6=77,ooo  volts. 

It  is  of  interest  to  compare  the  above  results  with  the  surge 
pressures  likely  to  be  set  up  upon  an  underground  cable  system. 
Take,  for  example,  a  three-core  2O,ooo-volt  cable  — 

LINE  PRESSURE  LINE 

PRESSURE.  TO  EARTH.  CURRENT. 

Volts.  Volts.  Amperes. 

(c)                ...          20,000  n.SS0  75 


io6 


Three-Phase  Transmission 


Normal  values  for  L  and  K  in  this  case  are  :— 

L  =  .748  x  io~3  henrys  per  conductor  per  mile. 

K  =  o.2ii  microfarad  Y  capacity  per  conductor  per  mile. 

Assuming  that  the  working  current  is  doubled  at  the 
moment  of  interruption,  and  that  the  value  of  the  pressure  V, 
is  at  its  maximum,  we  get  for  Vc — 

V<r=  V( 1 6330)2+ 79.8  x  10° 
=  18,650. 

The  insulation  between  cores  and  lead  sheath  would  thus  be 
subject  to  an  instantaneous  excess  pressure  of  18,650—16,340 
=  2,310  volts  under  the  conditions  assumed. 

Reflected  Waves.— If  A  B,  B  C,  and  c  D  (Fig.  41)  represent 
open  troughs  containing  water,  we  know  that  if  a  disturbance  at 

A          EJ         C          O 


FIG.  41. 

C  cause  a  wave  to  proceed  in  the  direction  c  D,  this  would,  on 
reaching  D,  be  reflected,  the  amplitude  of  the  wave  being 
increased  to  double  its  original  value. 

Suppose  a  similar  disturbance  to  take  place  at  A,  causing  a 
wave  to  travel  in  the  direction  A  to  B,  upon  reaching  B  the 
smaller  trough  B  c  will  be  unable  to  absorb  the  wave,  resulting 
in  an  increase  of  its  amplitude  which  may  be  nearly  twice  that 
of  the  original  wave.  A  wave  of  increased  amplitude  now 
traverses  the  trough  B  c,  and  is  similarly  increased  in  amplitude 
to  nearly  twice  its  value  at  the  point  C.  A  wave  of  four  times 
the  amplitude  of  the  original  disturbance  will  now  traverse  the 
trough  C  D,  and  will  finally  be  reflected  at  the  closed  end  D  with 
an  amplitude  approaching  eight  times  that  of  the  original  wave. 

A  transmission  line  may  be  considered  as   made  up  of  a 


Reflected  Waves 


TO: 


number  of  reactances  and  capacities  arranged  as  illustrated  by 
Fig.  42. 

If  the  switch  is  closed,  applying  a  high  voltage  to  the  cable 
instantaneously,  the  current  will  be  retarded  by  the  back  E.M.F., 
due  to  the  building  up  of  the  field  round  the  cable  cores,  and 
the  charging  up  of  the  cable  will  be  accomplished  gradually 
through  the  reactance  of  its  cores. 

The  current  will  increase  in  value  and  reach  its  maximum 
at  the  instant  the  cable  is  charged  up  to  the  applied  pressure. 
The  charge  having  reached  the  open  end  of  the  line  the  current 
tends  to  stop,  but  the  energy  stored  in  the  magnetic  field  of  the 
cable  due  to  its  self-induction  (corresponding  to  kinetic  energy 
in  a  moving  body)  now  tends  to  keep  the  current  flowing,  which 


FIG.  42. 

continues  to  charge  up  the  open  end  of  the  cable  to  double  the 
applied  pressure  or  thereabouts. 

A  wave  of  double  pressure  is  then  reflected  along  the  cable, 
and  the  potential  of  the  cable  will  oscillate,  as  shown  by  Fig.  43, 
until  it  gradually  settles  down  at  line  potential. 

If  the  self-induction  per  mile  of  one  core  of  a  transmission 
line  or  cable  is  "/"  henrys,  and  the  capacity  per  mile  of  core 

is  "  k "  farads,  it  may  be  shown  that  the  quantity  \J  r-.  repre- 
sents the  velocity  in  miles  per  second  with  which  an  electrical 
disturbance  would  be  propagated  along  the  core,  this  velocity 
being  so  great  that  the  resistance  of  the  cable  may  be  neglected. 
When  such  a  cable  is  switched  on  to  an  alternator,  electrical 
impulses  pass  into  the  cable  and  are  reflected  at  its  open  end. 
Should  it  happen  that  such  impulses  return  to  the  generator  end 


io8 


Three-Phase  Transmission 


of  the  cable  in  the  time  represented  by  one  half  period  of  the 
generator  wave,  we  get  conditions  favourable  to  resonance,  since 
the  reflected  waves  would  then  be  in  phase  with  the  generator 
waves.  In  other  words,  if  the  time  required  by  the  impulses  to 
travel  four  times  the  length  of  the  cable  corresponds  with  the 
periodic  time  of  the  alternator,  the  pressure  will  increase  due  to 
resonance  until  a  breakdown  of  the  insulation  occurs. 

As  an  example,  take  the  case  of  a  network  having  80  miles 
of  .05  three-core  2O,ooo-volt  cable,  we  may  assume  — 

/==  .748  x  io~3  henrys  per  mile  ; 


.2\\  x  io~6  farads  per  mile. 


40 


20 


V     10 


7\ 


Time. 


6 

FIG.  43. 


The  velocity  of  propagation  will  be 

V  ~kl=  79>6o°  miles  Per  second, 

and  the  frequency  of  the  natural  period  of  oscillation  is 

79600 

=  250  per  second. 


Hence,  with  an  alternator  giving  a  pressure  wave  of  50  cycles 
per  second,  and  having  a  pronounced  5th  harmonic  impressed 
upon  it,  we  should  expect  to  get  resonance  and  a  serious  rise  of 
pressure  from  this  effect. 


Concentration  of  Potential  109 

A  further  phenomenon  of  pressure  rise  or  concentration  of 
potential  is  very  much  in  evidence  on  most  systems  working  at 
extra  high  pressure.  If  we  have  a  loop  of  copper  wire  shaped 
as  in  Fig.  44,  it  is  well  known  that  a  static  discharge  passing 
from  A  to  B  will  jump  across  the  air-gap  in  preference  to 
traversing  the  metallic  shunt  to  the  air-gap  formed  by  the 
wire.  The  reason  being  that  a  self-induction  behaves  almost 
as  a  complete  insulator  when  subject  to  such  extremely  rapid 
oscillations  of  pressure  as  occur  with  static  discharges.  In  the 
case  of  transformers  or  motors  switched  on  to  high-pressure 
lines,  the  pressure  at  the  instant  of  switching  on  is  concentrated 
between  the  first  few  turns  of  the  windings.  Each  of  these 


FIG.  44. 

turns  has  a  self-induction,  a  capacity  to  the  next  turn  and  a 
capacity  to  earth  (Fig.  45),  and  until  these  capacities  become 
charged  up,  which  process  is  delayed  by  the  very  large  self- 
induction  effect  resisting  the  charge,  the  adjacent  turns  or  layers 
of  the  windings  upon  the  end  coils  may  have  to  withstand  the 
full  potential  of  the  circuit  concentrated  between  them. 

It  is  to  be  noted  that  precisely  the  same  effect  will  result  if 
one  terminal  of  the  transformer  or  motor  becomes  suddenly 
earthed  through  a  fault.  The  end  turn  in  this  case  will  be 
instantly  brought  to  earth  potential,  but  the  self-induction  of 
the  adjacent  turns  will  resist  the  immediate  change  of  condition 
resulting  in  a  high  potential  gradient  across  the  insulation. 

Various    remedies    have  been    suggested    for   reducing   this 


I  IO 


Three-Phase  Transmission 


effect,  probably  the  simplest  and  most  effective  being  to  pro- 
vide choking  coils  external  to  the  motor  or  transformer 
terminals  to  take  the  shock  at  switching  on,  &c. 

In  the  case  of  E.H.T.  transformers  also  there  is  another 
effect  met  with,  although  of  comparatively  rare  occurrence.  This 
is  the  current  rush  which  sometimes  occurs  upon  switching  the 
transformer  into  the  circuit,  resulting  in  a  pressure  rise,  and  is 
generally  explained  by  the  supposition  that  the  magnetic  con- 
dition of  the  iron  at  the  instant  of  switching  off  was  retained, 
and  of  such  sign  and  value  as  to  greatly  assist  instead  of  impede 
the  primary  current  at  the  instant  of  switching  on.  In  the  case 


A 

u 


FIG.  45. 

of  motors,  however,  the  slowing  down  of  the  rotor  generally 
tends  to  wipe  out  any  residual  magnetism  in  the  stator. 

Wave  Forms. — A  conductor  revolving  with  uniform  velocity 
in  a  uniform  magnetic  field  will  have  a  pressure  wave  of  true 
sine  form  impressed  upon  it,  and  if  we  plot  on  squared  paper 
its  values  at  equal  intervals  we  have  a  representation  of  what  is 
known  in  mechanics  as  a  pure  harmonic  motion.  Such  a  curve 
would  be  traced  by  a  pencil  attached  to  the  bob  of  a  heavy 
pendulum  under  which  a  piece  of  drawing  paper  was  moved 
with  constant  velocity  at  right  angles  to  the  direction  of  swing 
of  the  pendulum.  It  is,  however,  rarely  in  practice  that  a 
pressure  wave  of  this  form  is  obtained,  and  even  in  cases 


Irregular  Wave  Forms 


1 1 1 


where  an  alternator  develops  a  true  sine  pressure  wave,  the 
resultant  current  wave  will  often  have  a  form  which  is  con- 
siderably different  from  that  of  the  pressure  wave  owing  to  the 
fact  that  ordinary  circuits  in  practice,  such  as  those  containing 
arc  lamps  and  other  apparatus,  do  not  possess  constant  resistance 
or  reactance.  In  recent  years  effective  steps  have  been  taken  in 
the  design  of  alternators  to  produce  pure  sine  waves  by  the 
shaping  of  pole-pieces  on  the  rotors,  and  the  angular  spacing 
of  the  conductors  upon  the  stators  to  counteract  the  effects  of 
irregularities  in  the  magnetic  field  due  to  the  stator  slots.  Fig. 
46  shows  the  form  of  pressure  wave  of  a  generator  having  six 
stator  slots  per  pair  of  poles.  The  equation  of  the  curve  shown 
in  this  figure  may  be  expressed  in  the  form  : — 

V  =  A!  sin  (9  +  ^)  +  A3  sin  (3$  +  </>3)  +  A5  sin  (58  +  <£5),  &c. 

Where  A1}  A8,  A5,  &c.,  are  the  amplitudes  of  the  fundamental 
wave,  3rd,  5th,  &c.,  harmonics,  respectively,  and  ^,  <£2,  $3,  &c., 
give  the  phase  displacements  of  these  harmonics.  The  values 
of  Ap  A3,  &c.,  <f>v  <£3,  &c.,  for  the  wave  form  shown  in  Fig.  46, 
are  given  in  the  following  table  : — 


TABLE  XX. 


Order  of 
Harmonic. 

Amplitude  in 
Volts=A. 

Phase  Displacement 
in  Degrees  —  0. 

ISt       - 

6,750 

3rd     - 

148 

I56 

5th      -          - 

1,190 

171 

7th      - 

45 

75 

gth     - 

18 

27 

nth     - 

418 

166 

1  3th     - 

185 

131 

1  5th     - 

97 

1  08 

i;th     - 

270 

23 

It  will  be  noticed  that  the  most  important  harmonics  are 
the  5th,  nth,  and  I7th.  In  general,  if  there  are  p  slots  in  the 
stator  of  the  generator  per  pair  of  poles,  the  most  important 
harmonics  to  be  expected  are  the  (p—  i)th  or  the  (p+  i)th. 

If  we  plot  a  sine  wave  and  impose  on  it  an  even  harmonic 
(Fig.  47),  it  is  seen  that  the  two  halves  of  the  resulting  wave 


I  12 


Three-Phase  Transmission 


become  dissimilar,  and  we  deduce  from  this  that  even  harmonics 
will  not  be  present  in  the  pressure  waves  of  commercial  alter- 
nators. If  upon  the  fundamental  wave  we  impose  a  third 


FIG.  46. 

harmonic  or  any  harmonic  of  a  multiple  of  three  times  the 
fundamental  frequency,  the  three  pressures,  one  in  each  phase, 
become  superposed,  that  is,  they  all  act  in  the  same  direction  at 


EVEN  HARMONIC 


I  VHOO  S.n6 

n  V=20Sm  29 

IH   V=IOOSm6+20S.n26 


FIG.  47- 

the  same  instant  in  each  phase.  This  result  is  of  great  import- 
ance in  practice.  For  instance,  with  delta-connected  alternators 
and  a  pressure  wave  possessing  triple  frequency  harmonics,  idle 


Analysis  of  Wave  Forms  113 

currents  will  circulate  round   the  closed  mesh  formed  by  the 
three  delta-connected  windings. 

Again,  if  two  or  more  star-wound  alternators  with  earthed 
neutral  points  are  worked  in  parallel,  the  pressure  wave  of  one 
of  them  possessing  a  triple  frequency  harmonic,  whilst  those  of 
the  others  are  practically  sine  waves,  heavy  triple  frequency 
currents  may  result,  flowing  between  the  neutral  points  and 
the  phase  windings  of  each  machine.  In  order  to  avoid  this, 
the  practice  of  earthing  one  machine  only  in  the  station  has 
sometimes  been  adopted. 

The  writer  took  oscillograms  of  such  currents  on  a  three- 
phase  system,  and  found  that  they  varied  throughout  the  day 
with  the  nature  of  the  load  on  the  station,  and  according  to  the 
capacity  of  the  cables  and  self-induction  of  motors,  &c.,  on  the 
circuits.  It  was  found  that  capacity  currents  of  frequency 
3,  6,  9,  &c.,  times  the  fundamental  wave  were  flowing  between 
the  neutral  points  of  the  generators  and  earth.  An  account 
of  some  observations  made  upon  these  earth  currents  will  be 
found  in  the  Journal  of  the  Institute  of  Electrical  Engineers, 
Vol.  xxxiii.,  Part  166. 

The  complete  analysis  of  any  irregular  wave  form  may  be 
readily  effected  by  a  number  of  well-known  methods.  Space 
will  only  permit  here  of  the  description  of  the  following  simple 
and  approximate  method. 

Divide  the  complete  wave  from  o  to  360°,  or  both  positive  and 
negative  portions,  into  the  same  number  of  parts  as  the  order 
of  the  harmonic  it  is  desired  to  examine.  That  is,  if  we  wanted 
to  determine  the  amplitude  of  the  3rd  harmonic  with  reference 
to  the  fundamental  wave,  we  should  divide  the  complete  wave 
into  three  parts,  and  again  subdivide  the  zero  line  of  each  of 
these  three  parts  into  the  same  number  of  equal  divisions.  Add 
the  ordinates  of  each  of  the  three  parts  at  corresponding  divisions 
of  the  zero  axis,  and  divide  the  result  by  3  for  the  third  harmonic, 
5  for  the  5th  harmonic,  and  so  on.  These  results  will  give 
points  upon  the  harmonic  curve  which  can  then  be  plotted  on 
the  axes  of  the  pressure  waves  under  examination.  The  reason 
for  this  procedure  is  obvious,  since  the  addition  of  the  ordinates 
in  a  pure  sine  wave  divided  into  equal  parts  at  corresponding 
points  would  always  be  zero,  whereas  the  ordinates  of  the 
harmonics  would  have  equal  values  at  corresponding  divisions 
in  the  equal  parts  positive  and  negative,  and  hence  the  reason 
8 


Three-Phase  Transmission 


for  dividing  the  sum  of  the  ordinates  by  the  order  of  the 
harmonic  or  number  of  subdivisions  of  the  wave.  As  an 
example,  take  the  pressure  wave  illustrated  by  Fig.  48. 


too 


50 


30 


180 


270 


50 


100 


FIG.  48. 

To  determine  the  amplitude  of  the  3rd  harmonic,  we 
divide  the  curve  into  three  parts  as  shown.  We  then 
superpose  these  three  divisions  (Fig.  49),  and  add  corre- 


100 


3rd  HARMONIC 


100 


FIG.  49. 


spending  ordinates,  dividing  each  sum  by  3,  the  result  gives 
the  ordinate  of  the  3rd  harmonic  at  each  of  the  respective 
points.  It  is  to  be  noted,  however,  that  the  curve  so  obtained 


Variation  in  Wave  Form 


3RD  HARMONIC 


I.  V-  100  sin  0+20  sin  39 
fl.V=IOOsine  +  20  sin  (38*90) 
ffl.V- 100  sin9 +20  sin  (36 +  180) 


FIG.  50. 


5T-H  HARMONIC 


IV=IOO  5m  0+20  Sin  56 
II  VHOO  Sm  0  +  20  S.n  (50  +90) 


FIG.  51. 


n6  Three-Phase  Transmission 

may  not  be  a  true  sine  curve.  The  variation  in  wave  form  due 
to  any  particular  harmonic  as  its  displacement  relatively  to  the 
fundamental  wave  is  increased,  is  shown  by  Figs.  50  and  51. 
The  successive  curves  are  obtained  by  the  displacement  of  a 
third  and  fifth  harmonic  with  an  amplitude  of  one-fifth  of  the 
fundamental  by  90°  and  180°  respectively.  It  is  evident  that, 
according  to  the  displacement  of  the  harmonic  relatively  to 
the  fundamental  wave,  the  maximum  instantaneous  pressure 
may  be  increased  or  diminished.  This  brings  us  to  the  con- 

NON     INDUCTIVE 
RESISTANCE 


CURRENT 
TRANSFORMER 


sideration  of  what  is  known  as  the  form  factor  of  a  pressure 
wave. 

The  usually  accepted  definition  of  the  form  factor  of  a  pressure 
wave  is  the  ratio  of  the  maximum  ordinate  to  the  square  root 
of  the  mean  square  of  the  ordinates. 

Thus  for  a  sine  wave  the  form  factor  is    N/2=  1.414,  whereas 
for  peaky  waves  it  may  be  as  high  as  2. 

It  is  important  to  note  that  a  peaked  pressure  wave  will 
cause  less  core  loss  in  transformers,   motors,  &c.,  than  a  flat- 


Elimination  of  Harmonics  117 

topped  wave  for  the  same  effective  voltage,  for  with  a  peaked 
wave  the  effective  or  \/mean  square  value  becomes  greater  in 
proportion  than  the  mean  value. 

Since,  with  transformers  also,  the  pressure  developed  by  the 
secondary  winding  will  be  proportional  to  the  primary  current 
irregularities  of  the  wave  form  applied  to  the  primary  terminals 
and  accentuated  by  the  capacity  of  the  high-pressure  feeder 
cables,  will  be  reproduced  upon  the  low-pressure  voltage  wave 
of  the  secondary  circuits. 

It  is  often  of  importance  in  the  case  of  relays  and  protective 
gear  to  eliminate  harmonics  from  the  wave  form  of  the  secondary 
circuit  of  current  transformers.  This  is  usually  effected  by 


shunting  the  primary  winding  by  a  non-inductive  resistance  as 
shown  in  Fig.  52. 

In  this  case  the  high  frequency  currents  impressed  upon  the 
fundamental  wave  experience  greater  resistance  to  their  flow 
through  the  inductive  primary  winding  than  through  the  non- 
inductive  shunt,  and  in  this  way  ripples  in  the  secondary  current 
wave  tend  to  become  smoothed  out. 

Rotation   of   Harmonics. 

If  three  equal  E.M.Fs.,  ev  e.2,  e.#  at  phase  differences  of  120° 
be  connected  up  in  delta  (Fig.  53),  triple  frequency  harmonics 
will  act  in  the  same  direction  in  all  three  phases  at  the  same 


n8  Three-Phase  Transmission 

time,  and  will  produce  circulating  currents  in  the  closed  wind- 
ings. The  remaining  harmonics  differ  in  phase  by  120°  in  each 
of  the  three  windings. 

Thus  harmonics  I,  7,  13,  19,  25  combine  at  +120°  phase, 
whilst  harmonics  5,  11,  17,  23  combine  at  -  120°  phase.  This 
is  shown  graphically  by  Fig.  54. 

If  the  fundamental  wave  gives  a  rotating  field  in  one  direc- 
tion, harmonics  7,  13,  19,  25  will  give 


rotating  fields  in   the 


Rotation  of  Harmonics. 


90°  180° 

A,  B,  C-  PHASE  PRESSURES. 

A,  B,  C=ioosin0,  100  sin  (o  +  —\,  100  sin  (V*-— V 
V        3/  V    '   3/ 

D  =  5th  HARMONIC  =  20  sin  5  .  6  (Retreating). 
E-7th  HARMON ic  =  50  sin  7  .  6  (Advancing). 

FIG.  54. 

same  direction,  whereas  harmonics  5,  11,  17,  23  will  give  rotating 
fields  in  the  opposite  direction,  the  speed  of  field  rotation  being 
proportional  to  the  frequency  of  the  harmonic  in  each  case.  It 
will  thus  be  evident  that  the  presence  of  harmonics  may  have 
the  effect  of  diminishing  or  increasing  torque  in  induction  motors 
and  other  plant. 

Since  only  odd  harmonics  can  exist  in  the  wave  form  of 
commercial  alternators,  the  relative  frequency  of  these  will  be 
given  by  the  expression  (2K-i)«,  where  n  is  the  frequency  of 


General  Wave  Expressions  1  1  9 

the  fundamental  wave  and  K  has  successive  integral  values  from 
unity  upwards. 

The   pressure    wave    of   any   alternator   will,    therefore,   be 
represented  by  the  sum  of  all  such  terms  as  :  — 


Where    E,  is  the  amplitude  of  any  harmonic. 
j  is  the  order  of  the  harmonic. 
n  is  the  fundamental  frequency. 
Qj  is  the  phase  displacement  of  the  harmonic. 

If  the  circuit  to  which  this  pressure  wave  is  applied  is  of  a 
non-inductive  character  and  of  resistance  R,  the  current  wave 
will  be  given  by  the  sum  of  all  such  terms  as  :  — 


-y 

If  the  circuit  contains  a  constant  inductance,  the  impedance 
offered  to  higher  frequency  current  components  will  increase  in 
proportion  to  their  frequency,  and  these  will  tend  to  be  smoothed 
out  from  the  resulting  current  wave. 

If  the  circuit  includes  a  condenser  on  the  other  hand,  the 
impedance  offered  to  the  higher  frequency  current  components 
will  be  diminished,  and  accordingly  these  will  be  magnified  in 
proportion  to  their  frequency  in  the  resulting  current  wave. 
Moreover,  the  phase  displacement  of  the  current  components 
with  regard  to  their  corresponding  pressure  components  will  in 
each  case  vary  with  the  reactance  of  the  circuit. 

Now  for  a  sine  wave  the  effective  value  or  root  mean  square 
of  its  ordinates,  the  quantity  indicated  by  a  voltmeter  is  obtained 
by  dividing  the  maximum  ordinate  by  \/2,  hence  with  an 
irregular  wave  form  the  voltmeter  reading  will  represent  the 
square  root  of  the  sum  of  all  such  terms  as  — 


The  instantaneous  value  of  the  watts  is  obtained  by  multiply- 
ing the  instantaneous  values  of  the  volts  and  amperes,  and  is  — 

—  (2  Ej  sin  (2irjnt+  <?,•))-  for  a  non-inductive  load. 
K. 

The  average  value  of  this  in  the  case  of  an  inductive  circuit 
may  be  obtained  by  multiplying  the  ordinates  taken  from  current 


120  Three-Phase  Transmission 

and  voltage  oscillograms,  and  then  taking  the  mean.  If  capacity 
or  self-induction  be  present,  there  will  be  a  discrepancy  in  the 
values  so  obtained  for  reactive  and  non-reactive  circuits 
respectively. 

The  impedance  of  a  circuit  of  resistance  R,  self-induction  L, 
and  capacity  K  is — 


where       /L  is  that  part  of  the  reactance  due  to  self-induction  and  pro- 
portion to  the  frequency. 

-^  that  due  to  capacity  and  inversely  proportional  to  the 
/K 

frequency. 

Hence  the  impedance  of  the  circuit  to  an  harmonic  of  the 
nth  order  is  — 


It  may  be  of  interest  to   consider  at  this  point  the  varia- 
tion in  wave  form  produced  by  long  E.H.T.  cables.     We  may 


assume  that  a  number  of  generators  in  parallel  feeding  the  cable 
on  open  circuit  have  a  combined  self-induction  which  is  negligible. 

Take  the  case  of  a  20,000- volt  0.05  three-core  cable  50 
miles  in  length. 

The  Y  capacity  per  core  per  mile  is  .2 1 1  microfarad,  or  for 
50  miles  10.55  microfarads. 

The  self-induction  per  core  per  mile  is  .748  milli-henry,  or 
for  50  miles  37.4  milli-henrys. 

The  ohmic  resistance  per  core  per  mile  is  .858  ohm,  or  for 
50  miles  42.94  ohms. 


Wave  Distortion  by  Capacity 


121 


We  may  assume   with  close  approximation   that  the  total 
capacity  is  shunted  across  half  of  the  line,  as  in  Fig.  55. 


15 


05 


10 


N 

FIG.  56. 


If  the  frequency  n  for  the  fundamental  wave  is  50  ~  and 
p=2irn  ;  if  V:  =  voltage  at  condenser,  and  V  =  voltage  at  gener- 
ator, it  may  readily  be  shown  that 


V1 
V 


-/2(2/K  - 


Inserting  values  in  the  above  expression  and  denoting  by  N  odd 
multiples  of  the  fundamental  frequency,  we  get : — 


V1 


V      V  i  -  N%o34)  +  N4(.ooo376) 

Taking  values  of  N  =  i,   3,  5,  &c.,  in  succession,  we  get  cor- 

V1 
responding  values  of  -----  as  follows  : — 


122  Three-Phase  Transmission 

v1 
v 

i  1.016 

3  *-*° 

5  -         1-435 

7  2.06 

9  1. 18 

ii  0.64 

It  will  be  noted  from  the  above  ratios  that  the  amplitude  of 
the  5th  harmonic  is  increased  by  over  43  per  cent.,  whilst  that 
of  the  7th  harmonic  is  increased  .by  over  100  per  cent.  These 
results  are  shown  graphically  by  the  curve,  Fig.  56. 


CHAPTER  VI 
EARTHING 

IN  the  very  early  days  of  single-phase  alternate  current 
working  with  high  potentials  it  was  recognised  that  with  a 
completely  insulated  system  of  generator  and  cables,  the 
potential  to  earth  of  the  system  would  oscillate  about  a 
certain  value  represented  by  some  point,  such  as  O  in  Fig.  57, 
this  point  being  either  at  earth  potential  or  some  other 
potential  above  or  below  earth  depending  upon  whether  the 
system  as  a  whole  was  electrostatically  charged.  In  addition, 


Earth 


FIG.  57. 

that  the  position  of  the  point  O  would  depend  upon  the  leak- 
age from  the  poles  of  the  system  to  earth.  It  soon  became 
apparent  that  cables  which  would  prove  sufficiently  strong 
to  work  entirely  insulated  would,  should  their  insulation  become 
defective  on  one  pole  of  the  system,  be  subjected  to  a  much 
greater  pressure.  For  instance,  if  one  pole  of  the  generator 
became  earthed,  the  potential  in  this  case  would  oscillate  about 
the  point  o',  Fig.  58,  with  double  the  amplitude  of  that  in 
Fig-  57- 


124 


Three-Phase  Transmission 


The  practice  of  earthing  one  pole  of  the  alternator  per- 
manently was  then  adopted,  and  the  cable  insulation  made 
sufficiently  strong  to  withstand  the  maximum  variation  in  the 
potential  of  the  system  to  earth  likely  to  be  met.  This 
arrangement  also  proved  of  benefit  in  enabling  measuring 
instruments,  &c.,  to  be  inserted  in  proximity  to  the  earthed 
terminal  of  the  generator,  and  thus  kept  at  earth  potential. 

A  simple  method  for  determining  the  potential  of  partially 
insulated  systems  has  been  developed  by  Mr  M.  B.  Field.  The 
following  example  will  illustrate  the  principles  involved. 

In  the  diagram,  Fig.  59,  let  OA,  OB,  and  OC  represent  the 


+  2000 


-2000 


FIG.  58. 

E.M.Fs.  in  the  three  windings  of  a  star-wound  generator.  If 
the  windings  and  circuits  to  which  they  are  connected  are 
completely  insulated,  it  may  happen  that  no  part  of  the  system 
is  at  earth  potential.  If  the  pole  A  be  connected  to  earth  the 
diagram  may  be  considered  as  revolving  round  the  point  A  as 
centre  when  the  potentials  of  the  poles  C  and  B  relatively  to 
earth  will  be  given  by  the  lengths  of  the  vectors  AC  and  AB. 
If  the  three  poles  are  all  partially  insulated,  their  relative 
potentials  to  earth  will  similarly  be  given  by  the  revolution  of 
the  diagram  about  some  other  point,  such  as  o',  in  which  case 
the  line  oo'  represents  in  amplitude  and  phase  the  potential 


Earthing 


125 


of  the  neutral  point  of  the  windings,  and  lines  drawn  from  O'  to 
the  three  terminals  A,  B,  C  will  similarly  represent  in  amplitude 
and  phase  the  potentials  of  these  three  terminals  relatively  to 
earth. 

If,  therefore,  we  can  find  the  length  and  phase  relationship 
of  the  line  oo'  we  know  at  once  the  potentials  of  each  point 
of  the  system  relatively  to  earth. 

The  length  and  position  of  the  line  OO'  is  governed  by  the 
condition  that  the  sum  of  all  leakage  currents  flowing  to  earth 
is  zero  at  every  instant. 

A 


FIG.  59. 

It  may  be  readily  shown  that  the  position  of  the  point  O'  on 
the  diagram  is  the  same  as  the  centre  of  gravity  of  three  masses 
placed  at  A,  B,  and  C,  each  proportional  to  the  conductivity 
of  the  leakage  paths  to  earth  from  these  respective  terminals. 

As  an  example,  assume  the  star- wound  generator  (Fig.  59) 
connected  up  to  a  cable  system,  the  insulation  of  the  cores  in 
connection  with  each  terminal  being  as  follows  : — 

Terminal  A  =  60,000  ohms  conductivity  =  166  x  io~~° 
„          6  =  30,000      ,,  ,,  =334x10"° 

,,          C  =  20,000      „  „  =500x10"° 

The  sum  of  the  conductivities  is  thus  ipoox  io"G,  or  .0001,  and 


i26  Three-Phase  Transmission 

the  total  insulation  of  the  system  to  earth  is  10,000  ohms. 
Neglecting  capacity  currents  in  the  first  instance,  the  currents 
to  earth  from  A  and  ]?  alone  would  be  equal  if  the  line  AH 
revolving  around  the  point  D,  the  lengths  BD  and  AD  being  such 
that  BD  x  334=  AD  x  166,  or  AD  nearly  twice  BD. 

Further,  the  total  leakage  paths  from  A  and  B  of  conduc- 


tivity —    .         or         5  may  be  considered  as  concentrated  at 

the  point  D,  and  as  the  leakage  path  from  C  has  an  equal 
conductivity  the  point  P'  midway  along  the  line  CD  will  repre- 
sent the  point  at  earth  potential  of  the  system,  and  the  whole 
diagram  may  be  considered  as  revolving  round  the  point  r'  as 
regards  the  relative  potentials  to  earth  of  other  points  upon  the 

system. 

So  far  no  account  has  been 
taken  of  the  capacity  currents 
flowing  to  earth  from  the  three 
cores  of  the  cable  system  in 
connection  with  the  generator. 
These,  as  will  be  shown  later, 
determine  to  a  great  extent  the 
position  of  the  point  at  earth 
potential  on  the  diagram. 
FlG  g0  It  will  be  necessary,  however, 

to  first  consider  the  potential  of 

a  circuit  which  has  leakage  paths  to  earth  due  to  conductivity 
and  also  to  capacity. 

Take  the  case  of  a  single-phase  generator  whose  E.M.F.  is 
represented  by  the  rotation  of  the  vector  AB,  Fig.  60. 

If  we  have  paths  of  conductivity  to  earth  in  connection  with 
each  of  the  poles  AB,  the  point  at  earth  potential  will  be  in  some 
position  between  AB  as  already  explained.  Assume  now  that 
we  have  a  capacity  to  earth  of  K  farads  in  connection  with 
terminal  A,  and  a  path  to  earth  of  resistance  R  ohms  in  connection 
with  terminal  B. 

The  current  to  earth  through  the  capacity  at  A  will  be  90° 
in  advance  of  the  pressure  inducing  it,  whereas  the  current  to 
earth  through  the  resistance  at  B  will  be  in  phase  with  the 
pressure  inducing  it. 

The  position  of  the  zero  potential  point  must  be  such  that 
these  two  currents  are  equal  and  opposite  at  every  instant. 


Earthing  127 

It  will  be  found  that  the  locus  of  the  zero  point  is  a  semi- 
circle described  upon  the  line^AB  as  diameter. 

Assume  the  diagram  to  rotate  around  the  point  P  as 
centre,  then  the  length  of  the  vector  AP  will  represent  in 
phase  and  magnitude  the  pressure  acting  upon  the  capacity 
between  terminal  A  and  earth.  This  will  produce  a  current  90° 
in  advance  of  the  pressure  in  the  direction  PB',  and  of  amount 
27r?zK  x  (AP)  amperes.  On  the  other  hand  the  length  of  the 
vector  PB  represents  in  phase  and  magnitude  the  E.M.F.  acting 
upon  the  resistance  R,  and  inducing  a  current  in  it  of  amount 

/r>  p\ 

^-—^  amperes  in  the  direction  PB. 
i\. 

Now  the  condition  that  P  is  at  earth  potential  is  that  these 
currents  are  equal  and  opposite,  that  is 

APx 


AP 
BP 


P  we  get  the 


Tjr>  *,!/•  E> 

Dr       2Trnr^t\. 

If  \ve  drop  a  perpendicular  PC  from  the  point 
geometrical  relation  : — 

AC  =  AP_2  = 
CB~BP2~ 

We  may  now  proceed  to  consider  the  combined  effect  of 
capacity  and  resistance  in  the  case  of  the  star-wound  generator, 
whose  E.M.Fs.  are  shown  diagrammatically  by  Fig.  59. 

Assume  that  the  generator  is  connected  up  to  a  one-mile 
length  of  0.15  sq.  in.  three-core  5,ooo-volt  cable.  The  Y 
capacity  of  this  cable  per  core  per  mile  may  be  taken  at  0.285 
microfarad,  and  if  we  assume  a  frequency  of  50  cycles  we  get 
for  the  permittance  of  the  leakage  path 

2ir  x  50  x  .285  _89-4 
io6          ~~  io6' 

As  we  have  assumed  that  the  capacity  to  earth  in  connection 
with  each  terminal  of  the  generator  is  the  same,  which  would 
usually  be  the  case  in  practice,  we  may  consider  the  total 
capacity  leakage  paths  concentrated  at  the  central  point  O  of 
the  diagram,  and  of  permittance 

89.4  x  3_  268.2 
Io6      =~T^' 


128  Three-Phase  Transmission 

The  total  conductivity  leakage  paths  may  similarly  be  con- 
sidered as  concentrated  at  the  point  P'  as  before  and  of  amount 


Upon   OP'   describe   a   semicircle,  and  divide  OP'  at  a  point 
c'  such  that 


__ 

C'P'     \27mKR 


/  _  ^  _  y    *  . 

\27TX5ox  268.2  x  loooo/       7.18 


From  the  point  C'  draw  a  perpendicular  C'P  to  meet  the 
semicircle  at  the  point  P.  The  point  P  will  be  the  zero 
potential  point  on  the  diagram.  It  is  important  to  note  the 
considerable  stability  given  to  the  neutral  point  of  a  star-wound 
generator  by  the  presence  of  equal  capacities  of  comparatively 
small  amount  between  each  phase  and  earth  in  the  cable  system 
to  which  it  is  connected.  In  practice  there  would  usually  be 
a  much  greater  length  than  one  mile  of  cable  in  connection  with 
any  generator  running,  and  in  such  a  case  the  zero  potential 
point  of  the  system  would  be  indistinguishable  from  the  neutral 
point  of  the  generator,  in  spite  of  considerable  variation  in  the 
ohmic  resistance  between  each  phase  and  earth. 

The  argument  is  sometimes  put  forward  that  with  the 
neutral  point  of  the  system  insulated  there  is  less  danger  from 
shock  to  any  one  coming  accidentally  in  contact  with  one  pole 
of  the  system.  Since,  however,  the  effect  of  capacity  is  to  keep 
the  neutral  point  at  earth  potential,  an  attendant  making  contact 
between  one  pole  and  earth  through  his  body  would  receive 
practically  the  same  shock  as  if  the  neutral  point  of  the  gener- 
ator be  permanently  connected  to  earth. 

For  the  same  reason  electrostatic  voltmeters  connected 
between  each  pole  of  the  system  and  earth  will  not  indicate 
defective  insulation  until  this  becomes  so  low  that  a  breakdown 
results  immediately  the  voltmeters  show  an  appreciable  difference 
in  their  readings. 

If  the  vectors  OA,  OB,  and  OC  (Fig.  61)  represent  the 
E.M.Fs.  of  a  star-wound  generator  by  the  rotation  of  the  dia- 
gram about  the  neutral  point  O,  and  Oa,  Ob,  and  Oc,  represent 
the  amplitude  of  a  triple  harmonic,  it  is  obvious  that  since 
the  speed  of  rotation  of  Oa,  ob,  and  Oc  is  three  times  that  of 
A,  P,,  c,  whilst  the  line  OA  moves  from  the  position  OA  into  the 


Triple  Frequency  Currents 


129 


position  OB,  Oa,  ob,  and  Oc  will  have  made  one  complete  revolu- 
tion and  the  E.M.F.  Ob  will  now  act  on  OA  in  its  new  position  OB. 

We  see,  therefore,  that  at  the  same  instant  the  harmonic 
E.M.Fs.  are  acting  from  the  neutral  point  O  simultaneously  in 
all  three  phases  of  the  system. 

Accordingly,  if  equal  leakage  paths  exist  in  connection  with 
the  poles  of  a  generator  having  its  neutral  point  insulated,  the 
potential  of  the  neutral  point  will  be  raised  above  earth  by 
the  amount  of  the  triple  frequency  E.M.Fs. 

If  the  neutral  point  be  not  earthed,  and  the  insulation  of  the 
system  is  perfect,  the  triple  frequency  E.M.Fs.  will  balance  one 
another,  and   the   pressure  be- 
tween   the    neutral    point    and 
each    phase   will    not    contain 
triple  frequency  ripples. 

With  the  neutral  point  of 
the  generator  earthed,  however, 
the  triple  frequency  E.M.Fs. 
are  superposed  upon  the  pres- 
sure of  each  phase  winding, 
and  may  increase  or  diminish 
the  maximum  value  of  the 
pressure  wave  according  to  the 
phase  displacement  of  the  triple 
frequency  harmonics. 

The  pressure  between  phase 
and  earthed  neutral  being  expressed  by  V  where 

V  =  A  sin  tf  +  B  sin  36"  +  C  sin  96,  &c. 

it  has  been  shown  in  Chapter  V.  that  the  effective  value  of  this 
or  the  amount  indicated  by  a  voltmeter  is 

Vj  N/!(  A2  +  B2  +  C2,  &c.). 

Where  three-phase  star-wound  alternators  are  run  in 
parallel  with  earthed  neutral  points,  some  special  conditions 
have  sometimes  to  be  met  in  practice.  The  usual  connections 
are  illustrated  by  Fig.  62,  OO'  being  the  neutral  points  of  the 
generator  windings,  AB  a  neutral  bar  earthed  through  the 
resistance  R.  The  objects  of  earthing  are  threefold  in  the 
case  of  three-phase  generators  feeding  transmission  circuits: 
(i)  To  maintain  the  correct  relative  potential  between  each 
9 


FIG.  61. 


130 


Three-Phase  Transmission 


phase  and  earth  ;  (2)  To  restrict  the  current  through  a  fault  on 
the  cable  system  to  that  sufficient  to  operate  the  circuit  breakers 
clearing  the  fault ;  (3)  To  dissipate  electrostatic  charges  pro- 
duced by  external  or  internal  influences. 

It  will  be  evident  that  if  the  wave  form  of  one  machine 
differs  from  that  of  the  others  in  possessing  pronounced  triple 
frequency  harmonics,  heavy  currents  may  circulate  within  the 
closed  circuits  formed  by  the  windings  of  the  machines  in 
parallel.  Moreover,  the  direction  of  these  triple  frequency 


i 

L° 

( 

o' 

1 

X" 

x 

« 

X" 

"vj 

• 

A  - 

i  «  , 

—  R 

E 

FIG.  62. 

currents  in  the  phase  windings  being  such  as  to  produce 
opposite  magnetising  effects  upon  the  stator  iron,  the  parallel 
circuit  of  three  branches  between  each  neutral  point  will  tend 
to  be  non-inductive. 

Various  devices  have  been  adopted  and  proposed  for 
preventing  these  triple  frequency  circulating  currents.  In 
some  cases  the  neutral  point  of  one  machine  alone  is  earthed. 

The  use  of  choking  coils  and  a  combination  of  choking 
coils  and  condensers  has  also  been  suggested,  placed  between 
the  neutral  points  of  the  generators  and  the  earthed  bar.  It  is 


Triple  Frequency  Currents  131 

evident  that  the  impedance  to  triple  frequency  currents  offered  by 
a  choking  coil  possessing  approximately  constant  self-induction 
would  be  nearly  three  times  that  opposed  to  currents  of  funda- 
mental frequency,  and  hence  the  circulating  currents  would  be 
damped  out  to  a  greater  extent  than  currents  of  normal  frequency 
to  earth  due  to  a  short  circuit  on  the  cable  system. 

The  combination  of  a  suitably  proportioned  capacity  and 
self-induction  in  the  earth  circuit  is  also  interesting,  since  this 
combination  can  be  tuned  to  offer  practically  no  impedance  to 
currents  of  normal  frequency,  whilst  possessing  considerable 
impedance  for  currents  of  triple  frequency. 

A  further  method  of  eliminating  these  circulating  currents 


FIG.  63. 

consists  in  the  employment  of  three  single-phase  transformers 
having  a  ratio  of  3  to  I,  the  secondary  windings  being  con- 
nected in  series  between  the  neutral  point  of  the  generator 
with  irregular  wave  form  and  the  earthed  bar.  The  resultant 
triple  frequency  E.M.F.  is  thus  made  to  cancel  that  existing 
between  the  neutral  point  of  the  generator  and  earth. 

Three  delta-connected  transformers  are  frequently  employed 
for  feeding  a  transmission  line  ;  under  normal  conditions,  with 
equal  leakage  currents  from  each  line  and  assuming  the  absence 
of  electrostatic  charges  from  lightning,  &c.,  we  may  consider 
the  potential  of  the  transformer  windings  relatively  to  earth,  as 
given  by  the  rotation  of  an  equilateral  triangle  about  its  centre 
of  gravity  O,  as  in  Fig.  63. 


132 


Three-Phase  Transmission 


If  from  any  reason,  however,  the  leakage  current  from  any 
one  line  is  much  in  excess  of  that  from  the  other  two,  the  axis 
of  rotation  of  the  triangle  will  be  transferred  from  the  point  O 
to  a  point  near  the  pole  O',  and  the  whole  triangle  will  rotate 
about  this  point  (Fig.  64).  In  this  case  it  will  be  seen  that 
the  high-pressure  windings  of  the  transformers  will  be  charged 
alternately  plus  and  minus  to  the  full  potential  between  line 
wires. 

Now,  the  low-pressure  winding  of  the  transformers  and  ad- 


FIG.  64. 

jacent  high-pressure  windings  will  possess  considerable  electro- 
static capacity.  Moreover,  if  the  generator  feeding  the  low- 
pressure  windings  is  entirely  insulated  from  earth,  an  additional 
capacity  will  exist  between  the  generator  windings  and  primary- 
windings  of  the  transformers  and  earth.  We  shall,  accordingly, 
have  the  condition  of  things  represented  by  Fig.  65. 

The  total  line  pressure  will  be  divided  between  the  two 
condensers  A  and  B  in  series  in  the  inverse  ratio  to  the  capacities. 

As  an  example,  assume  a  5,ooo-volt  generator  having  a 
capacity  between  windings  and  earth  of  .003  microfarad  per 


Effect  of  Earth  on  Line  133 

phase,  whilst  the  capacity  between  the  windings  of  each  trans- 
former is  .001  microfarad.  It  is  evident  that  with  a  line 
pressure  of  60,000  volts  the  generator  insulation  may  be  sub- 
jected to  a  pressure  of  15,000  volts,  whilst  the  insulation  between 
the  windings  of  the  transformers  will  be  subjected  to  a  pressure 
of  45,000  volts. 

A  pressure  of  three  times  the  working  pressure  would  be 
very  severe  upon  the  generator  insulation  and  likely  to  cause 
breakdown,  whereas  by  the  simple  expedient  of  earthing  the 
neutral  point  this  danger  would  be  averted. 


15000' 


4-5.000' 


II 

Generator 
Frame         t 

Generator  wind 
\  mg&  Transfr: 
Primary 

I'    Transfr.  Secondary 
B    &  Line 

FIG.  65. 

Similar  considerations  will  exist  as  regards  the  receiving  end 
of  the  line  where  step  down  transformers  are  employed. 

With  transformers  wound  for  very  high  potentials  such  as 
100,000  to  200,000  volts,  the  windings  are  found  to  possess  con- 
siderable capacity,  and,  in  addition,  more  or  less  self-induction 
due  to  magnetic  leakage. 

When  one  pole  of  the  high  tension  winding  of  such  a  trans- 
former is  earthed,  and  the  other  pole  is  on  open  circuit,  the 
capacity  current  will  be  a  maximum  at  the  point  where  the 
windings  join  the  earth  connection. 


134  Three-Phase  Transmission 

If,  on  the  other  hand,  both  poles  of  the  high  tension  winding 
are  insulated  and  the  mid-point  of  this  winding  is  available,  it 
will  be  found  that  the  maximum  value  of  the  capacity  current 
is  at  the  mid-point  of  the  winding. 

The  capacity  currents  in  the  E.H.T.  secondary  windings  of 
such  transformers  on  open  circuit  react  upon  the  primary 
magnetising  current,  and  in  some  cases  may  render  this  a 
leading  current  instead  of  a  lagging  one. 

It  may  thus  happen  that  resonance  occurs  due  to  the 
capacity  and  self-induction  of  the  H.T.  windings  causing  very 
considerable  and  sudden  rises  of  pressure. 

A  type  of  extra  high-pressure  transformer  designed  by  the 
Oerlikon  Company  is  illustrated  by  Fig.  66.  The  transformer 
is  enclosed  in  an  oil  tank,  and  pipe  coils  for  circulating  cooling 
water  are  arranged  in  the  upper  layers  of  oil.  This  type  of 
transformer  is  used  for  normal  working  pressures  of  40,000  volts 
and  upwards. 

Where  long  transmission  lines  are  used  to  convey  power  for 
lighting  and  industrial  purposes  to  densely  populated  towns,  it 
will  generally  be  necessary  to  terminate  the  overhead  lines  at  a 
substation  outside  the  town,  the  supply  being  then  transformed 
to  lower  pressure  and  distributed  to  other  substations  within  the 
town  itself  by  an  underground  network  of  cables.  In  such  cases 
it  is  of  the  utmost  importance  to  protect  the  underground  cables 
at  the  point  where  they  are  connected  to  the  overhead  con- 
ductors through  the  transformers.  In  these  cases  the  principle 
of  earthing  through  a  resonant  circuit  has  also  been  effected 
with  success.  The  substation  building  containing  the  trans- 
formers, switchgear,  &c.,  is  made  to  form  a  metallic  cage  by 
means  of  wire  netting  enclosed  in  the  walls  of  the  building  and 
effectively  earthed  throughout.  Each  of  the  transmission  lines 
is  then  connected  through  a  resonant  circuit  consisting  of  a 
condenser  and  self-induction  in  series  to  the  earthed  metal  cage. 
The  resonant  circuits  are  tuned  to  some  value  between  the  usual 
frequencies  met  with  due  to  lightning  discharges  or  high 
frequency  power  surges,  and  of  the  order  of  50,000  to  one  million 
per  second,  to  which  they  will  offer  little  impedance.  For  the 
ordinary  working  frequency  of  the  transmission  line,  however, 
the  impedance  of  these  resonant  earth  circuits  will  be  almost 
infinite.  In  this  way  complete  protection  to  the  cable  system 
has  been  secured. 


High  Pressure  Transformers 


FIG.  66. 


136  Three-Phase  Transmission 

In  cases  where  the  distribution  of  power  to  consumers  is 
carried  out  by  three-phase  four-core  cables,  complete  protec- 
tion of  the  low-pressure  distributing  mains  from  abnormal  rise 
in  pressure,  due  to  leakage  from  the  E.H.T.  circuits  of  the 
system,  is  obtained  by  joining  up  the  secondary  windings  of 
the  transformers  in  star  with  the  neutral  point  of  transformers, 
and  the  fourth  neutral  conductor  of  each  distributing  main  con- 
nected to  an  earthed  bar  at  the  substation.  Where  the  low- 
pressure  distribution,  however,  is  also  carried  out  by  means  of 
overhead  conductors  or  three-core  cables,  additional  safety 
devices  may  be  required  to  safeguard  against  leakage  from  the 
extra  high-pressure  portions  of  the  system.  Such  devices 
usually  take  the  form  of  star-connected  electro-magnets  with 
shaded  poles  operating  relay  discs.  The  neutral  point  is 
earthed  and  the  other  end  of  each  magnet  winding  connected 
to  one  of  the  three  phases  of  the  distributing  mains.  Any 
abnormal  rise  in  pressure  causing  a  disturbance  of  the  relative 
potential  between  the  low-pressure  conductors  and  earth  will 
thus  operate  the  relays  and  cut  off  the  low-pressure  supply. 


CHAPTER   VII 
LINE    APPLIANCES 

Supports. — Line  supports  are  required  to  resist  stresses  under 
ordinary  conditions  due  to  the  following  : — 

(1)  Weight  of  wires  assumed  to  act  vertically. 

(2)  Wind  pressure  on  wires  assumed  to  act  horizontally. 

(3)  Wind  pressure  on  pole  and  brackets  and  insulators. 

If  the  direction  of  the  line  changes  abruptly  the  resultant 
stress  upon  the  support  due  to  the  tension  in  the  wires  is 
usually  counteracted  by  the  employment  of  extra  stays  or 
stronger  supports. 

Occasionally  the  supports  will  be  subject  to  unbalanced 
stresses  due  to  broken  wires,  but  under  normal  conditions 
stresses  due  to  wind  pressure  on  the  supports  and  wires  are 
the  chief  considerations.  For  long  spans,  lattice-work  iron 
towers  (Fig.  67)  are  now  coming  into  general  use,  and  possess 
several  advantages. 

In  designing  an  overhead  line  for  power  transmission  at 
high  pressure,  the  Board  of  Trade  require  that  a  maximum 
wind  pressure  of  30  Ibs.  per  square  foot  be  allowed  for  acting 
normally  to  any  flat  surface.  In  the  case  of  cylindrical  sur- 
faces, the  wind  pressure  is  found  to  be  only  about  one-half  to 
two-thirds  of  that  on  a  flat  surface.  In  calculating  the  effect  of 
wind  pressure,  therefore,  it  is  usual  to  take  half  of  the  projected 
surface  in  the  case  of  wooden  poles  and  two-thirds  of  the  pro- 
jected surface  in  the  case  of  the  wires. 

If         R  =  mean  radius  of  a  pole  in  inches. 

L  =  length  of  pole  out  of  ground  in  inches. 
L!  =  height  from  ground  to  centre  of  wires  in  inches. 

•p  T 

The  wind  pressure  at  30  Ibs.  per  sq.  ft.  =  -    -  Ibs. 

4.8 

As  the  resultant  pressure  acts  at  a  point  approximately  half 


138 


Three-Phase  Transmission 


*— ' 


A\\\\\\\\\\\\\\\\\\\\\X\\\V 

17  ->| 


Fir,.  67. 


Wind  Pressure  on  Wires  139 

the  height  of  the  pole,  the  equivalent  pressure  acting  at  the 
centre  of  the  wires  is  :  — 

RL      L   =  RL2 

4.8  x  2L1~9.6  L; 

Similarly,  it  may  be  shown  that  the  wind  pressure  on  a  single 
wire  is  1.67  a?S  taking  two-thirds  of  its  cylindrical  diameter, 

where  d=  diameter  of  wire  in  inches. 

S  =  length  of  span  in  inches. 

The  Board  of  Trade  Regulations  require  that  the  maximum 
stress  in  overhead  wires  at  a  temperature  of  22°  Fahr.  and  with 
a  maximum  wind  pressure  of  30  Ibs.  per  square  foot  shall  not 
exceed  one-fifth  of  the  breaking  stress  of  the  wire.  It  is 
usual  to  assume  that  the  curve  taken  by  a  suspended  wire  is 
a  parabola,  when  the  tension  due  to  the  weight  of  the  wire  alone 
is  given  by  :  — 

W  .  P 
8.  S   ; 

where  W  =  weight  in  Ibs.  per  foot. 

/=  length  of  span  in  feet. 
S  =  sag  of  wire  in  feet. 

This  formula  also  holds  for  any  other  consistent  units  of  length 
employed. 

For  copper  the  tension  in  pounds  is  given  approximately  by  :  — 

5.8  x  area  square  inch,  x  (span  in  feet)2 
Sag  in  inches 

As  there  will  be  a  certain  amount  of  elastic  extension  of  the 
wire,  the  sag  will  be  more  than  given  by  this  formula.  The 
testing  of  the  elasticity  of  any  given  wire  is  readily  carried  out, 
however,  in  practice  by  observation  of  the  sag  over  different 
lengths  of  span. 

The  tension  due  to  wind  pressure  of  30  Ibs.  per  square  foot 
with  a  suspended  wire  of  diameter  d,  all  lengths  being  taken  in 
the  same  units,  is  :  — 


and  the  tension  due  to  the  resultant  of  weight  of  wires  and  wind 
pressure  is  :— 


140  Three-Phase  Transmission 

It  is  obvious  from  the  above  formula  that  smaller  wires 
experience  greater  stresses  proportionally  than  those  of  larger 
diameters. 

The  correct  design  of  metal  lattice  work  and  other  types  of 
supports  for  overhead  transmission  lines  involves  a  number  of 
considerations  common  to  all  engineering  structures,  and  fully 
dealt  with  by  purely  mechanical  treatises.  It  is  only  proposed 
to  consider  here  briefly  some  of  the  simplest  types  of  supports, 
and  to  indicate  a  few  of  the  general  principles  underlying  their 
construction. 

It  is  shown  in  books  on  mechanics  that  if  a  bending  moment 
equivalent  to  a  weight  W  suspended  at  the  end  of  an  arm  of 
length  /  acts  at  any  section  of  a  beam  having  moment  of  inertia 

I,  the  material  will  be  stressed  to  the  extent  -r-  at  I  in.  from 

the  neutral  line  of  the  section.  If  the  edge  of  the  section  is 
n  inches  away  from  the  neutral  line,  the  maximum  stress  will 
be  n  times  this  amount,  and  should  this  stress  exceed  the  break- 
ing stress  of  the  material  fracture  will  occur. 

The  quantity  -  is  generally  called  the  strength  modulus  of 
the  section. 

For  rectangular  sections  this  is  given  by  — 

bd^ 
6  ' 
where  />  =  breadth  and  d=  depth. 

For  a  circular  section,  the  strength  modulus  is  _ 


where  R  is  the  radius  of  the  section. 

If  we  denote  by  F  the  breaking  stress  of  the  material  in 
pounds  per  square  inch,  the  bending  moment  M  at  fracture  for 
a  rectangular  support  fixed  at  one  end  and  loaded  at  the 
other  is  — 


, 
6 

and  for  a  support  of  circular  section  it  is— 


Strength  of  Fir  Poles  141 

The  value  of  F  having  once  been  obtained  from  a  destruc- 
tive test  of  one  support,  the  bending  moment  by  which  any 
similar  support  will  be  ruptured  may  be  calculated. 

From  a  number  of  tests  of  fir  poles  it  was  found  that  the 
load  in  pounds  VV  which,  applied  at  a  height  of  L:  inches  above 
ground  level  to  a  pole  of  radius  R  inches  at  ground  level,  would 
produce  fracture,  could  be  expressed  by  the  following  formula  :  — 


We  have  also  seen  that  the  equivalent  wind  pressure  w  on 
a  pole  acting  at  a  height  of  Lj  inches  from  this  ground  level  was 

RL2 


9.6 


Ibs. 


Hence,  with  a  factor  of  safety  of  ten,  the  net  strength  which  is 
available  for  resisting  lateral  wind  pressure  on  the  wires  is 


_    6,2.8*!  - 


9.6 

It  is  desirable  that  the  taper  of  poles  is  such  that  the  radius 
at  the  top  is  not  less  than  two-thirds  of  the  radius  at  ground 
level  to  ensure  that  the  greatest  strength  occurs  at  this  point, 
which  is  most  subject  to  decay. 

The  deflection  of  a  support  fixed  at  one  end  and  loaded  at 
the  other  is  given  by 

D-lW 

3EI' 

where  E  =  Young's  Modulus. 

I  =  moment  of  inertia  of  the  section. 

The  value  of  I  for  a  circular  section  is 


Hence  we  may  write  :  — 

D      /    4    \WLj- 
^' 


The  deflection  of  a  standard  support  having  once  been 
ascertained  by  test  and  the  value  of  the  constant  term  in  ' 
brackets  determined,  the  deflection  of  any  support  of  similar 
type  and  material  can  then  be  calculated. 


142 


Three-Phase  Transmission 


Great  stresses  sometimes  occur  due  to  the  breaking  of  all 
the  line  wires  in  one  span,  resulting  in  a  heavy  pull  on  the 
supports  by  the  tension  of  the  wires  in  those  spans  near  the 
break  which  are  not  interrupted.  If  a  support  is  flexible  in 
the  direction  of  the  line,  the  tension  in  the  wires  will  be  much 
reduced  by  the  bending  of  the  supports,  and  probably  by  the 
foundations  giving  also  to  some  extent.  The  support  will 
deflect  in  such  cases  until  the  tension  of  the  wires  is  equal  to 
the  elastic  resistance  of  the  support. 

From  a  number  of  tests  of  fir  poles,  the  deflection  (D)  was 
found  to  be  approximately  : — 

i         WL3 


I) 


3456000    R4 


A  Poles. — These  (Fig.  68)  should  have  an  8  in.  by  4  in. 
creosoted  brace  block  6  to  8  ft.  in  length  fixed  about  2  ft.  from 
the  butt  end,  and  at  the  top  the 
two  legs  should  be  scarfed  together, 
about  one-third  of  each  pole  being 
cut  away.  An  oak  key  6  in.  deep 
let  into  each  member  [  in.  to  i  £  in. 
about  two-thirds  from  the  top  of 
the  scarf  prevents  slipping. 

The  spread  of  A  poles  should 
be  about  one-eighth  of  the  length. 

An  A  pole  is  four  and  a  half 
times  as  strong  as  a  single  pole 
similar  to  those  composing  its 
members. 

The  wind  pressure  on  an  A 
pole  is  taken  as  one  and  a  half 
times  that  on  a  single  pole. 

The  deflection  in  the  direction 
of  the  wires  is  only  about  half 
that  of  a  single  pole. 

Taking  average  values  of  tests 
by  Professor  Goodman,  it  appears 
that  the  transverse  deflection  of  an 

A  pole  is  about  one-fiftieth  that  of  a  single  pole  of  the  same 
dimensions  as  those  composing  its  members.  Considerable 
variation  is  likely  to  occur,  however,  owing  to  slip  at  the 


FIG.  68. 


Strength  of  Cross  Arms 

joint.      The    majority    of    poles    tested    to    destruction 
through  the  buckling  of  the  compression  leg. 


failed 


Cross  Arms. — The  length  of 
cross  arm  depends  upon  a  number 
of  considerations  in  the  case  of 
long  high  voltage  transmission 
lines.  These  have  already  been 
referred  to  in  Chapter  I. 

On  short  medium  pressure 
lines  the  possibility  of  short 
circuit  due  to  the  swaying  of  the 
wires  in  the  wind  becomes  of 
importance.  Birds  are  also  likely 
to  cause  short  circuit  on  such 
lines. 


FIG.  69. 


-L 


The  Breaking  Stress   w  of  a  Rectangular  Oak  Cross  Arm 
(Fig.  69)  is  given  by 


where  W  =  weight  in  cwts.  at  the  extremity  of  the  cross  arms, 

L  =  length  of  arm  in  inches. 
B  =  breadth  in  inches. 
D  =  depth  in  inches. 
C  =  A  constant  =17  approximately. 

Economical  Span.  —  The  total  cost  of  overhead  lines  is  made 
up  of:  — 

Cost  of  wires. 
„       supports. 
„       insulators. 
„       erection. 
„       wayleaves  capitalised. 

In  the  case  of  any  particular  overhead  line  the  cost  of  the 
supports  will  be  proportional  to  the  number  employed.  Way- 
leaves  will  also  largely  depend  upon  the  number  of  supports 
adopted. 

If,  however,  the  number  of  supports  is  decreased,  they  must 
be  made  stronger  and  higher  to  resist  increased  wind  pressure, 
and  to  give  sufficient  headroom.  The  cost  of  labour  during 
erection  will  also  be  increased  per  support. 


144  Three-Phase  Transmission 

It  is,  therefore,  apparent  that  there  is  a  most  economical 
span  which  can  be  adopted  with  any  given  set  of  electrical 
requirements. 

It  is  found  that  over  a  fair  range  of  spans,  however,  the 
total  cost  is  fairly  constant. 

The  stress  on  supports  due  to  change  in  the  direction  of 
the  wires  may  be  ascertained  as  follows.  If  the  wires  make  an 
angle  <£  at  the  support  B  (Fig.  70),  the  total  tension  in  directions 
BA  and  BC  will  be  nt,  where  «  =  the  number  of  wires,  and  /  =  thc 


tension  of  each  wire  in  Ibs.     The  resultant  T  of  these  two  forces 
in  the  direction  BD  is 

T  =  znt  cos  -  Ibs. 

2 

The  stress  in  practice  would  usually  be  taken  up  by  a 
galvanised  steel  stay  wire  consisting  of  seven  or  nineteen  strands 
of  No.  8  S.W.G.  wire. 

If  in  Fig.  71  T  =  resultant  stress  in  line  wires  as  before, 
S  =  stress  in  stay  wire, 
<£  =  the  angle  the  stay  wire  makes  with  the  support, 

then  S  =  -JI_  Ibs. 

sin  <f> 

If  the  stay  wire  cannot  be  fixed  to  the  support  at  the  same 
level  as  the  line  wires  (Fig.  72) — 


Stay  Wires 


Let  H  =  height  of  line  wires  above  ground. 

h  =  height  at  which  stay  wire  is  fixed. 

Then  S=  ^—  .    ?. 

sin  $        h 

It  is  to  be  hoped  that  much  greater  facilities  than  hitherto 
will  be  extended  to  promoters  of  transmission  schemes  in  this 
country  in  the  near  future. 

The  Board  of  Trade  Regulations  requiring  high  factors  of 
safety  largely  increase  the  cost  of  construction  of  overhead 
lines,  and  the  difficulties  of  obtaining  wayleaves  often  militate 
seriously  against  an  economical  transmission  of  power  into 
rural  districts. 


FIG.  71. 


\\\\ 
FIG.  72. 


A  further  obstruction  sometimes  arises  from  the  powers 
conferred  upon  Local  Authorities  to  veto  overhead  wires,  and 
some  amendments  of  these  legal  powers  of  obstruction  are 
sorely  needed. 

Telephones. — With  all  extra  high-pressure  transmission  and 
distribution  schemes  in  this  country  the  Board  of  Trade  insist 
upon  adequate  telephonic  communication  being  provided  between 
the  generating  stations,  distributing  stations,  and  substations  of 
the  system  respectively.  This  is  usually  carried  out  by  multi- 
core  paper  and  air-insulated  telephone  cables,  lead-covered  and 
armoured,  laid  direct  in  the  ground.  These  telephone  cables  are 
in  most  cases  of  necessity  laid  alongside  the  high-pressure  feeder 
cables  traversing  the  same  route,  and  a  certain  amount  of 


146  Three-Phase  Transmission 

interference  is  sometimes  found  to  occur  between  the  telephone 
and  high-pressure  circuit.  In  the  writer's  experience,  where  the 
neutral  points  of  the  generators  at  the  power  station  are  earthed, 
such  interference  in  some  cases  has  been  traced  to  the  in- 
sufficiently insulating  qualities  of  the  small  wires  run  between 
the  telephone  cable  dividing  boxes  and  the  instruments 
themselves.  It  must  be  remembered  that  with  irregular  wave 
forms  containing  triple  frequency  harmonics  the  lead  sheaths 
of  the  feeder  cables  are  subject  to  electrostatic  charges  of  high 
frequency,  and  in  spite  of  the  usual  earthing  arrangements  small 
sparks  may  often  be  obtained  between  the  cable  sheaths  and 
neighbouring  metallic  objects.  With  overhead  transmission 
lines  working  at  pressures  of  100,000  volts  the  telephone  lines 
are  usually  run  upon  an  independent  set  of  poles. 

With  lines  working  at  lower  pressures,  however,  it  is  common 
practice  to  run  the  telephone  wires  at  about  10  feet  below  the 
line  conductors  attached  to  insulators  carried  by  the  line 
supports.  Electro-magnetic  induction  is  largely  prevented  by 
the  transposition  of  both  the  line  conductors  and  the  telephone 
conductors  themselves. 

Where  the  line  transformers  are  arranged  in  delta  connection, 
however,  a  further  precaution  against  electrostatic  effects  is 
sometimes  adopted.  This  consists  in  joining  the  telephone 
wires  by  split  choking  coils  at  each  end  of  the  line,  the  mid 
points  of  these  choking  coils  being  connected  to  earth. 

Lightning  Arresters. — The  types  of  lightning  arresters  in 
most  general  use  for  protecting  transmission  lines  may  be 
described  briefly  under  the  following  headings  : — 

1.  Electrolytic. 

2.  Water  jet. 

3.  Multigap. 

4.  Horn  gap. 

The  electrolytic  form  of  lightning  arrester  which  is  now  very 
extensively  used  is  based  upon  the  principle  that  aluminium 
immersed  in  a  suitable  electrolyte  becomes  coated  with  a  film 
which  will  only  allow  a  small  current  to  pass  until  a  certain 
voltage  is  reached,  approximately  400.  After  this  voltage  is 
exceeded  the  film  breaks  down,  allowing  a  large  current  to 
pass,  but  upon  the  reduction  of  the  voltage  the  film  is  again 
reformed. 


Lightning  Arresters  147 

A  large  number  of  circular  dished  shaped  trays  of  aluminium 
are  fitted  one  within  the  other,  but  separated  by  suitable 
insulated  washers. 

The  space  between  the  trays  is  filled  with  electrolyte,  and 
the  whole  enclosed  in  an  earthenware  jar.  For  high  voltages  a 
number  of  such  jars  are  mounted  one  above  the  other,  and 
connected  in  series  with  a  horn  gap  between  each  line  and  earth. 

With  the  water-jet  type  of  arrester  water  is  allowed  to  spray 
upwards  and  impinge  upon  horizontal  metallic  plates  in  direct 
connection  with  the  line  wires.  It  is  generally  only  employed 
at  the  generating  station  end  of  the  transmission  line  or  at 
substations  where  a  plentiful  supply  of  water  is  available. 
Although  this  type  of  arrester  has  been  found  to  work  well  on 
the  Continent  it  entails  a  loss  of  power  by  reason  of  leakage 
from  the  transmission  line,  and  for  this  reason  it  would  appear 
to  be  the  usual  practice  to  shut  off  the  water  unless  thunder- 
storms are  expected. 

In  the  case  of  the  multigap  arrester  a  number  of  small  metal 
cylinders  are  employed,  separated  by  small  air  gaps,  the  number 
of  gaps  being  made  sufficient  to  prevent  arcing  after  a  discharge 
from  line  to  earth  has  taken  place.  In  some  forms  of  this 
arrester  about  twice  the  number  of  gaps  required  to  resist  the 
line  voltage  are  employed  in  series  with  a  resistance  to  earth. 
In  addition  a  shunt  resistance  is  placed  across  the  half  of  the 
air  gaps  remote  from  the  line. 

The  horn  type  of  arrester  (Fig.  73)  consists  of  wires  placed 
in  a  vertical  plane  at  an  angle  between  them,  the  air  gap  being 
least  at  the  bottom,  but  increasing  upwards.  One  of  the  wires 
is  connected  to  the  line,  and  the  other  to  earth  usually  through 
a  water  resistance.  The  space  between  the  horns  at  the  bottom 
is  adjusted  to  withstand  a  discharge  at  a  certain  margin  over  the 
normal  pressure  between  line  and  earth. 

Generally  speaking,  in  the  case  of  long  transmission  lines 
lightning  arresters  are  only  installed  at  the  ends  of  the  line,  or 
at  substations.  It  is  now  becoming  the  usual  practice,  however, 
to  run  an  earthed  wire  the  whole  length  of  the  transmission 
line  situated  at  some  distance  above  the  line  conductors,  and 
earthed  at  frequent  intervals. 

Choke  Coils. — An  important  accessory  to  every  overhead 
transmission  line  is  the  choke  coil  or  self-induction  spiral. 


148  Three-Phase  Transmission 


FIG  73 


Choke  Coils 


149 


FIG.  7. 


1 50  Three-Phase  Transmission 

Each  line  «{ter  passing  the  lightning-  arresters  ut  the  entrance 
to  the  generating  station  or  substation  passes  through  a  choke 
coil  (Fig.  74),  generally  consisting  of  two  flat  spiral  coils  of 
copper  placed  side  by  side,  and  connected  in  parallel.  These 
coils  are  usually  supported  in  mid  air  by  porcelain  insulators, 
but  in  some  cases  are  immersed  in  oil.  The  special  feature  of 
lightning  and  other  static  disturbances  on  transmission  lines  is 
the  extreme  rapidity  with  which  they  occur,  and  their  very 
high  frequency  of  oscillation.  It  has  been  computed  that  the 
frequency  of  a  lightning  discharge  may  be  several  million 
periods  per  second,  and  probably  is  seldom  less  than  50,000 
periods.  Accordingly  choke  coils  which  at  the  normal  frequency 
of  25  to  60  periods  of  the  supply  would  be  practically  non- 
inductive,  behave  as  insulators  to  impulsive  rushes  of  current, 
and  rapidly  oscillating  discharges.  Hence  by  placing  suitable 
choke  coils  on  each  line  upon  entering  the  generating  station, 
and  after  the  line  has  passed  the  lightning  arresters,  most  static 
disturbances  will  be  dissipated  through  the  lightning  arresters. 
Choke  coils  are  shown  in  position  in  Fig.  1 2. 

Power  Factor  Correction. — The  power  factor  of  a  circuit 
is  usually  denned  by  the  ratio  of  true  watts,  as  measured  by 
a  wattmeter,  to  the  apparent  watts  obtained  by  the  product  of 
the  effective  or  \/mean2  amperes  flowing  in  the  circuit  by  the 
potential  difference  in  effective  volts  across  its  terminals.  With 
sine  waves  of  pressure  and  current  the  power  factor  is  also  given 
by  the  value  of  the  cosine  of  the  angle  of  phase  difference 
between  the  pressure  and  current  waves  respectively.  The  power 
factor  can  never  be  greater  than  unity,  and  in  the  case  of  most 
alternating-current  circuits  met  with  in  practice  is  less  than 
unity. 

With  irregular  wave  forms  of  pressure  and  current  the 
power  factor  of  the  circuit  will  be  dependent  upon  other  char- 
acteristics, these  being  the  angles  of  phase  difference  between 
corresponding  harmonics  present  in  the  pressure  and  current 
waves  and  variation  in  proportionality  between  such  harmonics. 
It  is,  therefore,  evident  that  the  phase  difference  between  an 
irregular  pressure  and  current  wave  as  determined  by  the  points 
at  which  they  cut  the  horizontal  axis  respectively,  cannot  be 
used  to  determine  the  power  factor  of  the  circuit,  since  the 
positions  of  these  zero  points  may  be  altered  considerably  by 


Low  Power  Factor  151 

the  presence  of  certain  harmonics,  as  we  have  already  seen  in 
Chapter  V. 

Generally  speaking,  if  we  find  the  fundamental  sine  com- 
ponents of  the  pressure  and  current  waves  by  harmonic  analysis, 
we  shall  find  also  that  the  phase  difference  between  them  largely 
determines  the  value  of  the  power  factor  of  the  circuit,  the 
effect  of  other  harmonics  often  being  inappreciable. 

In  all  cases  where  the  power  factor  of  a  circuit  is  low,  due  to 
phase  difference  between  pressure  and  current,  it  is  possible  to 
raise  it  by  placing  a  suitable  condenser  or  self-induction  as  a 
shunt  across  the  circuit,  but  in  special  cases,  where  low  power 
factor  is  due  to  wave  distortion,  this  method  cannot  be  adopted. 

The  two  principal  causes  of  low  power  factor  in  practice 
are : — 

(1)  Self-induction  of  load  and  line. 

(2)  Capacity  of  line. 

The  extent  to  which  the  regulation  of  an  overhead  trans- 
mission line  may  be  affected  by  these  quantities  has  already 
been  discussed,  and  it  is  now  proposed  to  review  briefly  the 
practical  means  available  to  raise  the  power  factor  of  a  circuit. 

The  effect  of  low  power  factor  upon  extensive  systems 
employing  expensive  underground  mains  and  many  sub- 
stations may  be  very  serious,  and  accordingly  may  justify 
considerable  capital  expenditure  towards  rectifying  the  defect. 

For  instance,  the  steam  plant  in  the  generating  station  may 
be  prevented  from  working  up  to  its  full  rated  capacity,  due  to 
the  fact  that  the  output  of  the  alternators  is  limited  by  the 
heating  of  their  windings,  and  the  demagnetisation  of  their  field 
magnets  by  the  large  lagging  currents. 

Moreover,  the  inductive  drop  in  the  cable  system  with  low 
power  factor  will  greatly  exceed  that  at  unity  power  factor. 

The  C2R  loss  in  the  cables  will  indeed  vary  inversely  as  the 
square  of  the  power  factor,  thus  with  a  power  factor  of  0.5  the 
C2R  loss  will  be  four  times  that  with  power  factor  unity. 

As  regards  the  substations  themselves  the  regulation  of  the 
transformers  may  be  seriously  affected  by  low  power  factor  and 
the  capacity  of  both  transformers  and  switchgear  heavily  handi- 
capped. 

Where  the  low  power  factor  of  the  system  is  due  to  a  highly 
inductive  load  such  as  that  formed  by  a  number  of  induction 
motors  working  considerably  under  full  load  at  the  end  of  the 


152 


Three-Phase  Transmission 


line,  the  generators,  line,  &c.,  may  be  relieved  of  the  wattless 
component  of  the  current  by  shunting  the  load  by  a  suitable 
condenser,  or  applying  its  equivalent  in  the  form  of  a  syn- 
chronous motor  over-excited,  or  by  the  employment  of  rotary 
converters.  This  arrangement  is  represented  diagrammatically 


FIG.  75. 

by  Fig.  75  ;  the  wattless  component  of  the  current  in  this  case 
only  circulates  locally  between  the  load  and  the  shunt  formed 
by  the  condenser  or  its  equivalent. 

On  the  other  hand,  if  the  low  power  factor  is  due  to  the 
electrostatic  capacity  of  a  long  overhead   transmission  line  at 


FIG.  76. 

light  loads,  the  generators  alone  can  be  relieved  of  the  wattless 
component  of  the  current  by  shunting  the  line  with  a  suitable 
self-induction  as  shown  diagrammatically  by  Fig.  76. 

In  reviewing  the  practical  means  available  for  correcting  low 
pcwer  factor  upon  an  existing  system,  it  is  first  to  be  noted  that 
the  extent  of  the  correction  required  will  vary  from  time  to  time 


Power  Factor  Correction 


with  the  load  throughout  the  day.  Accordingly,  in  those  cases 
where  induction  motors  are  the  cause  of  the  trouble,  and  the 
employment  of  condensers  is  adopted,  it  will  probably  be  found 
most  convenient  to  arrange  that  each  of  the  larger  units  be 
provided  with  its  own  condenser  which  can  be  switched  on  to 
the  supply  circuit  simultaneously.  If  synchronous  motors  or 
rotary  converters  be  used,  however,  a  certain  amount  of  hand 
regulation  will  generally  have  to  be  faced.  The  manufacture 
of  condensers  suitable  for  extra  high-pressure  working  has 


/R 


FIG.  77. 

already  attained  considerable  success,  the  principal  factors 
militating  against  their  more  extended  use  being  high  initial 
cost  and  the  difficulty  of  dissipating  the  heat  produced  in  the 
dielectric  under  working  conditions. 

For  correction  of  low  power  factor  due  to  the  electrostatic 
capacity  of  long  transmission  lines,  large  inductances  have  been 
successfully  employed  to  relieve  the  generating  plant  in  some 
cases  of  thousands  of  apparent  kilowatts  represented  by  the 
large  charging  current  flowing  into  the  line  at  the  high  working 
pressure  adopted. 


154  Three-Phase  Transmission 

With  an  existing  load  of  induction  motors  at  the  end  of 
a  transmission  line,  resulting  in  a  low  power  factor  of  the 
system,  the  most  efficient  means  of  correction  will  usually  be 
found  in  the  adoption  of  over-excited  synchronous  motors 
"  floated  "  or  working  on  the  line  at  the  receiving  end,  and  in 
close  proximity  to  the  load.  It  may,  therefore,  be  of  interest  to 
consider  here  some  features  upon  which  the  success  from  a 
financial  point  of  view  of  this  method  of  power  factor  correction 
will  depend. 

In  Fig.  77, 

Let       OA  =  E.M.F.  of  generator. 
OB  =  back  E.M.F.  of  motor. 
OC  =  current  in  circuit. 

OQ  =  PR  =  back  E.M.F.  of  self-induction  of  circuit  =/LC. 
OR  =  CR  loss  in  circuit. 

Then  'OP  =  E.M.F.  required  to  drive  the  current  C  round  the  circuit, 
and  the  phase  difference  between  OA  and  OB  must 
be  such  as  to  give  OP  as  a  resultant. 

From  the  figure  it  is  evident  that  the  output  of  the  generator 
is  OA  x  OC  X  cos  oc  watts,  whilst  the  power  used  by  the 
motor  is  OBxOCxcos/3  watts  in  furnishing  power  and  over- 
coming friction  losses,  &c.  Since  OB  and  PA  are  equal  and 
parallel  it  is  evident  that  their  projections  Ob  and  Ra  are  equal, 
and,  therefore,  the  difference  between  Oa  and  Ob  is  OR,  and 
OC  x  OR  is  the  power  lost  in  resistance. 

In  Fig.  78  let  the  resultant  pressure  OP  have  the  same  value 
and  phase  as  before,  and  hence  the  current  C  remain  the  same, 
but  let  the  counter  E.M.F.  of  the  motor  OB'  be  greatly  increased, 
keeping  the  point  B'  in  the  same  vertical  line  £B,  so  that  the 
power  used  by  the  motor  OB'xOC  cos  )8'  will  remain  the  same 
as  before.  In  this  case  the  phase  position  of  the  impressed 
E.M.F.  OA'  required  to  complete  the  parallelogram  will  lie  on 
the  reverse  side  of  the  axis  OA  to  that  in  the  case  of  Fig.  77, 
that  is,  the  current  OC  will  now  be  in  advance  or  lead  the 
impressed  pressure  OA'. 

We  see,  therefore,  that  by  over-exciting  a  synchronous  motor 
so  that  the  counter  E.M.F.  exceeds  the  impressed  E.M.F.,  the 
current  in  the  circuit  will  lead  the  impressed  E.M.F. 

From  the  same  diagram  it  may  be  deduced  that  there  are 
two  values  of  the  counter  E.M.F.  or  excitation  for  which  the 


Synchronous  Motor  155 

current  in  the  circuit  will  be  the  same,  lagging  or  leading  the 
same  impressed  pressure  by  equal  angles.  Moreover,  for  a 
certain  value  of  counter  E.M.F.  or  excitation  the  current  in  the 
circuit  will  be  a  minimum. 

As  an  example  of  power  factor  correction  by  means  of  a 
synchronous  motor  we  may  take  the  case  of  a  generating 
station  with  an  output  of  4,000  kilovolt-amperes  at  a  total  power 
factor  of  0.7,  and  assume  that  it  is  desired  to  raise  this  power 
factor  to  0.9. 


FIG.  78. 

Take  any  horizontal  line  OX  (Fig.  79)  to  represent  the 
phase  of  the  pressure  at  the  generating  station,  and  with 
radius  OA  =  4,000  units  describe  an  arc  of  a  circle  AB. 
Upon  OX  mark  off  a  length  OC  =  2,800  units,  and  from  C 
draw  CD  at  right  angles  to  OX,  cutting  the  arc  AB  at  the 
point  D.  The  length  OC  will  now  represent  the  true  power 
in  the  system,  2,800  kilowatts.  CD  will  represent  the  wattless 
component  of  the  power,  2,860  kilovolt-amperes,  and  the  length 
OD  the  total  output  of  the  station  in  kilovolt-amperes  at  0.7 
power  factor. 

Upon  OX  mark  off  a  length  OE  =  3,600  units,  and  from  th 


156 


Three-Phase  Transmission 


point  E  draw  EF  at  right  angles  to  OX,  cutting  the  arc  AB  at 
the  point  F. 

The  length  OE  will  now  represent  true  power  in  the  system 
to  the  extent  of  3,600  kw.,  EF  will  represent  the  wattless 
component  of  the  power  1,746  kilovolt-amperes,  and  OF  will 
again  represent  the  total  output  of  the  station  of  4,000  kilovolt- 
amperes  at  0.9  power  factor.  Now,  in  order  that  the  power 


FIG.  79. 

factor  of  the  system  may  be  raised  from  0.7  to  0.9,  it  is  obvious 
from  the  diagram  that  the  difference  between  the  lagging  com- 
ponents CD  and  EF,  or  1,1 14  kilovolt-amperes,  must  be  counter- 
acted by  a  leading  component  of  like  amount  furnished  by  the 
synchronous  motor.  From  the  point  C  erect  a  perpendicular 
CG  on  the  line  OX  of  length  1,114  units,  this  will  represent  the 
leading  wattless  component  to  be  furnished  by  the  synchronous 
motor.  We  now  require  to  estimate  the  real  power  required  to 


Synchronous  Motor  157 

overcome  friction,  windage,  iron  and  copper  losses  in  the  motor 
running  light.  Assume  this  to  be  IOO  kw.  and  mark  off  CH  of 
length  100  units  in  phase  with  the  pressure  OX.  CH  then 
represents  real  power  lost  in  the  motor.  Join  GH,  which  will 
be  found  on  measurement  to  be  approximately  1,120  units  and 
gives  the  kilovolt-ampere  rating  of  the  synchronous  motor, 
which,  floated  on  the  line,  will  raise  the  power  factor  of  the 
system  from  0.7  to  0.9. 

The  first  thing  to  be  noted  in  connection  with  the  above 
calculation  is  that  although  the  useful  capacity  of  the  generating 
plant  has  been  increased  by  800  kw.,  this  has  been  effected  by 
the  necessary  capital  outlay  upon  an  1,120  K.V.A.  synchronous 
motor,  and  in  addition  the  running  cost  of  100  units  of  electrical 
energy  per  hour.  This  brings  us  to  the  all-governing  question 
with  any  scheme  for  power  factor  correction,  "  Will  it  pay  ? " 
As  already  indicated,  the  answer  will  depend  in  any  particular 
case  upon  the  capital  cost  of  plant  mains  and  substations 
running  charges,  &c.,  which  expert  investigation  will  alone 
interpret.  It  still  remains  to  point  out  one  important  feature  ; 
if,  as  is  rarely  the  case  in  practice,  it  is  possible  to  allocate  to 
the  synchronous  motor  definite  and  continuous  work,  a  com- 
paratively small  increment  in  its  kilovolt-ampere  rating  will 
enable  it  to  do  much  useful  work,  and  thus  considerably  reduce 
the  standing  and  running  charges  otherwise  attributable  to  its 
installation. 

For  instance,  if  we  join  GE  in  Fig.  79  we  find  this  length 
scales  1,373  units,  and  this  represents  the  kilovolt-ampere  rating 
of  a  synchronous  motor  capable  of  furnishing  a  leading  wattless 
component  of  1,114  kilovolt-amperes,  and  useful  work  to  the 
extent  represented  by  the  length  HE,  namely,  700  kw.  We 
thus  see  that  by  increasing  the  rating  of  the  synchronous  motor 
by  253  kilovolt-amperes,  we  enable  it  to  do  useful  work  to  the 
extent  of  700  kw. 

As  regards  the  effect  of  low-power  factor  upon  the  generating 
station  itself,  it  will  generally  be  found  that  it  is  cheaper  to 
instal  a  larger  generator  than  a  synchronous  motor.  In  some 
cases  where  the  existing  alternators  have  been  unable  to  work 
up  to  the  full  load  of  the  engines  to  which  they  were  coupled, 
larger  generators,  but  coupled  to  the  same  sized  engines  as 
before,  were  subsequently  installed.  By  over-exciting  the  new 
generators  the  wattless  current  required  was  supplied  by  them, 


158  Three-Phase  Transmission 

and  the  whole  of  the  steam  plant  thus  enabled  to  work  up  to  its 
full  rated  capacity. 

Where  the  conditions  are  such  that  rotary  converters  can  be 
employed,  this  plant  possesses  advantages  over  the  synchronous 
motor  as  regards  efficiency  and  reliability  in  working,  and  for 
a  small  increase  in  its  kilovolt-ampere  rating  it  will  supply  a 
very  considerable  leading  wattless  component  for  the  correction 
of  low-power  factor. 

Of  recent  years  considerable  attention  has  been  given  to 
the  improvement  of  the  induction  motor,  which  may  be  said 
to  be  the  chief  cause  of  low-power  factor  upon  existing  supply 
systems.  This  has  resulted  in  the  development  of  commutating 
forms  of  induction  motors  in  which  the  power  factor  may  be 
made  practically  unity.  With  such  motors  a  special  exciter 
is  combined,  consisting  of  a  commutating  alternate  current 
generator  whose  magnets  are  excited  by  the  low  frequency  rotor 
currents. 

Boosting. 

It  was  pointed  out  in  Chapter  II.  that  the  question  as  to 
whether  it  will  pay  to  employ  boosting  upon  one  or  more 
feeders  leaving  the  generating  station  will  depend  upon  the 
working  cost  of  the  boosting  appliances  employed,  with  the 
particular  load  curve  to  be  met,  as  compared  with  the  interest 
and  sinking  fund  charges  upon  the  cost  of  the  extra  copper 
which,  if  put  into  the  feeders,  would  render  boosting  un- 
necessary. 

The  cost  of  attendance  upon  boosting  appliances  installed 
at  the  generating  station  ends  of  feeders  will,  in  general,  be 
slight,  whereas,  if  installed  at  the  substation  ends  of  the  feeders, 
the  cost  of  attendance  may  become  a  considerable  item. 

As  an  example  of  boosting,  we  may  take  the  case  of  a 
2,ooo-volt  single-phase  feeder  transmitting  300  kw.  to  a  sub- 
station six  miles  distant,  as  follows  : — 

Distance  of  transmission 6  miles. 

Load  transmitted— Single-phase  P.P.  .  i        -         -         -  300  kw. 

Maximum  bus  bar  pressure  at  generating  station  -         -  2,200  volts. 

Working  pressure  at  substation  -         -         -  2,ooo  volts. 

Full  load  current  I5o  amperes. 

Load  factor         -  .         .  I3  per  cent. 


Boosting,  Financial  Considerations        159 

As  alternative  schemes  we  could  adopt  in  this  case : — 
Scheme  A  (with  Booster) — 

One  0.15  sq.  in.  concentric  cable  with  CR  drop  510  volts. 

Less  pressure  supplied  by  booster  -  310      „ 


Scheme  B  (without  Booster) — 

Two  0.2  sq.  in.  concentric  cables  with  CR  drop       -      200  volts. 

It  is  to  be  noted  that  under  Scheme  A  the  energy  to  be 
supplied  by  the  booster  is 

310  volts  x  150  amperes  =  46. 7  kw. 
We  may  assume  the  following  relative  capital  expenditure  : — 

Scheme  A — 

Six  miles  0.15  sq.  in.  2,2oo-volt  V.B.  C.C.  cable  laid 

in  cast-iron  trough,  reinstatement  ist  setts  £9>°54 

50  kw.  regulating  booster,  erected  complete     -  150 

£9,204 
Scheme  B — 

Twelve  miles  0.2  sq.  in.  22oo-volt  V.B.  C.C.  cable 

laid  in  cast-iron  trough,  reinstatement  ist  setts     £16,956 

The  annual  charges  may  now  be  set  out  as  follows : — 


160  Three-Phase  Transmission 

TABLE   XXI. 


With  Booster. 

Without  Booster. 

Standing  Charges. 

£       s.     d. 

£     s.    d. 

Interest  and  sinking  fund  per  annum  on 

capital  cost  of  cables  laid  complete,  at 

6  per  cent.   - 

543    5    ° 

1,017     7     3 

Interest   and   sinking  fund    per   annum 

upon  capital  cost    of  boosting   trans- 

former and  switchgear,  at  6  per  cent.  - 

900 

Interest  and  sinking  fund  at  6  per  cent. 

upon    proportion   of  generating   plant 

representing     losses     in     cables     and 

boosting  transformer  at  .£35  per  kw. 

installed 

162    12      0 

63    o    o 

Running  Charges. 

Value  of  C2R  loss  per  annum  in  cables 

and    boosting    transformer  at   works, 

running  cost  of  o.375d.  per  unit    - 

103    12      0 

39  1  6    o 

Value  of  open  circuit   losses,  dielectric 

and  copper  losses  in  cables,  iron  and 

copper  losses  in  boosting  transformer, 

at  works  running  cost  of  o.375d.  per 

unit 

7    8     5 

5     4    o 

825  17     5 

I>12S     7     3 

Saving  per  annum  by  adopting  boosting,  ^299.  95.  lod. 


APPENDIX  A 


BOARD  OF  TRADE  REGULATIONS  FOR 
OVERHEAD  WIRES 

i.  Maximum  Intervals  betzveen  Supports. — The  interval  be- 
tween any  two  wooden  poles  used  singly  as  supports  for  an 
overhead  line  shall  not  exceed  200  ft. ;  provided  that  where  the 
line  makes  an  angle  at  any  such  pole  the  interval  between  that 
and  the  next  pole  shall  not  exceed  150  ft.  In  the  case  of 
supports  other  than  single  wooden  poles  the  intervals  between 
the  supports  shall  be  such  as  may  be  prescribed  by  the  Board  of 
Trade. 

2.  Factors  of  Safety. — Every  support    for  an  overhead  line 
shall  be  of  a  durable   material,  and   shall  be  properly  stayed 
against  forces  due  to  wind  pressure,  change  of  direction  of  the 
line,  or  unequal  lengths  of  span.     The  factor  of  safety  shall  be 
for  overhead  lines  at  least  5,  and  for  wooden  poles  at  least  10, 
and  for  iron  or  steel  structures  at  least  6,  taking  the  maximum 
possible  wind  pressure  at  50  Ibs.  per  square  foot.     No  addition 
need  be  made  for  a  possible  accumulation  of  snow. 

3.  Attachment  of  Overhead  Lines. — All  overhead  lines  shall 
be  attached  to  insulators,  and  shall   be  so  guarded   that  they 
cannot  fall  away  from  the  support. 

4.  Height  from  Ground,  &c. — An  overhead  line,  placed  after 
the  date  of  these  Regulations,  shall  not  in  any  part  thereof  be  at 
a  less  height    from  the    ground  than   22  ft.,  except  with  the 
consent  of  the  Board  of  Trade,  and  shall  not  be  accessible  to 
any  person  without  the  use  of  a  ladder  or  other  special  appliance  ; 
and,  in  the  case  of  a  high-pressure  overhead  line  so  placed,  no 
part  thereof  which  crosses  a  street  shall  be  at  a  less  height  from 
the  ground  than  25  ft.,  except  with  the  consent  of  the  Board  of 
Trade. 


1 62  Three-Phase  Transmission 

5.  Three-wire  System. — Where  a  supply  is  given   by  over- 
head lines  on  the  three-wire  system,  the  positive  and  negative 
conductors  shall  be  placed  side  by  side  above  the  intermediate 
conductor.      The  intermediate  conductor  shall  consist  of  two 
wires  placed  side  by  side  at  a  distance  apart  greater  than  that 
between  the  positive  and  negative  conductors,  and  connected  in 
each  span  by  two  cross  wires  placed  in  such  a  manner  that  in 
the  event  of  either  the  positive  or  negative  conductor  breaking, 
it  shall  fall  on  one  at  least  of  the  cross  wires. 

6.  Supply  from  Two-wire  System. — Where  a  supply  is  given 
by  overhead  lines  from  a    two-wire  system,  with  the  negative 
conductor  connected  with  earth,  the  positive  conductor  shall  be 
placed  above  the  negative  conductor  in  such  a  manner  that  in 
the  event  of  breakage  it  must  fall  on  the  negative  conductor. 

7.  Service   Lines  from    Overhead  Lines. — Service  lines  from 
overhead  lines  shall  be  led  as  directly  as  possible  to  insulators 
firmly  attached  to  some  portion  of   the  consumer's    premises 
which  is  not  accessible   to   any  person  without  the  use  of  a 
ladder  or  other  special  appliance.     Every  portion  of  any  service 
line  which  is  outside  a   building  but  is  within  7  ft.  from  the 
building,  shall  be  efficiently  protected  by  insulating  material. 

8.  Angle   of  Crossing  Thoroughfares. — Where  an  overhead 
line  crosses  a  street,  the  angle  between  the  line  and  the  direction 
of  the  street  at  the  place  of  crossing  shall  not  be  less  than  60°, 
and  the  spans  shall  be  as  short  as  possible. 

9.  Lines  Crossing  Metallic   Substance. — Where  an  overhead 
line   crosses,   or   is    in    proximity   to,  any    metallic   substance, 
precautions   shall    be   taken    by   the    Undertakers   against   the 
possibility  of  the  line  coming  into  contact  with  the  metallic 
substance,  or  of  the  metallic  substance  coming  into  contact  with 
the  line  by  breakage  or  otherwise. 

10.  Discharge  of  Pressure  in  Case  of  Fire.—lr\  the  case  of 
any  high-pressure  overhead  line  exceeding  one  half  mile  in  total 
length,  means  shall  be  provided  whereby  in  case  of  fire  or  other 
emergency  the  pressure  may  be  discharged  from  any  portion  of 
the  line  erected  over  or  alongside  of  any  building  or  buildings. 

11.  Maintenance. — Every  overhead    line,  including  its   sup- 


B.O.T.  Regulations  163 

ports  and  all  the  structural  parts  and  electrical  appliances  and 
devices  belonging  to  or  connected  with  the  line,  shall  be  duly 
and  efficiently  supervised  and  maintained  as  regards  both 
electrical  and  mechanical  conditions. 

1 2.  Disused  Overhead  Lines  to  be  Removed. — The  Undertakers 
shall  remove  any  overhead  line  upon  ceasing  to  use  it  for  the 
supply  of  energy,  unless  upon  so  ceasing  they  satisfy  the  Board 
of  Trade  that  they  intend  to  bring  it  into  use  again  within  a 
reasonable  time. 

13.  Overhead   Lines. — Overhead    lines    shall    not    after   the 
date  of  these  Regulations  be  erected  or  maintained  except  in 
accordance  with  plans  approved  by  the  Board  of  Trade,  and 
subject   to    such    Regulations    as    the    Board    may   prescribe ; 
provided  that  this   Regulation  shall  not  apply  to  any  electric 
lines  which  have  been  erected  at  the  date  of  these  Regulations 
so  long  as  those  lines  are  maintained  in  accordance  with  any 
Regulations    of  the    Board  of  Trade  which   are   in    force   and 
applicable  thereto  at  that  date,  and  with  any  requirements  of 
the  Board  made  thereunder. 

These  Regulations  are  made  subject  to  the  power  of  the 
Board  of  Trade  to  make  such  further  or  other  Regulations  as 
they  may  think  expedient. 

Consents  for  Overhead  Wires. — Applications  for  consent 
for  overhead  wires  are  considered  in  each  case  on  its  merits 
The  following  information  should  be  given  : — 

1.  Where  the  Undertakers  are  a  Company,  evidence  of  con- 
sent of  Local  Authorities  where  the  wires  cross  any  road.     The 
Local  Authorities  are  : — (a)  In  England  and  Ireland  :  Borough 
Councils,  Urban  District  Councils,  and  Rural  District  Councils ; 
($)  In    Scotland  :    Police   Commissioners,    Gas    Commissioners, 
Town  Councils,  and  County  Councils. 

2.  A  statement  showing  commercial  or  other  considerations 
why  underground  cables  should  not  be  used. 

3.  A  brief  description  of  the  proposed  system. 

4.  Is  the  supply  to  form  (i)  an  extension  of  an  existing 
system   or  underground   cables,  or  (2)  of  an  existing  traction 
system,  or  (3)  an  independent  system  ? 


164  Three-Phase  Transmission 

5.  A  plan  on  a  scale  of  about  6  in.  to  the  mile,  showing  the 
proposed  route  of  the  overhead  wire.     (In  the  case  of  Ordnance 
maps,  the  sheets  to  be  sent  separately.) 

6.  In   the  case  of  high  and  extra  high  pressure,  plans  of 
construction  of  poles,  &c.,  on  a  scale  of  about  i  in.  to  the  foot. 

Note, — Proposals  for  high  or  extra  high-pressure  wires  carried 
alongside  roads  cannot  be  entertained,  the  transmission  lines 
must  go  across  open  country. 


APPENDIX    B 


SELF-INDUCTION    OF    WIRES 

FROM  purely  theoretical  considerations  it  may  be  shown  that 
the  self-induction  in  henrys  per  kilometre  of  two  parallel  wires 
L  is  given  by  the  expression  : — 

L=  (0.1+0.92  Iog10  -J  ID- 3  -  (i) 

Where  d=  distance  between  the  centres  of  the  wires. 

r  =  radius  of  the  wires,  r  and  d  being  expressed  in  similar 
units. 

For  a  single  core  of  a  three-phase  line  this  reduces  to 


The  above  expressions,  however,  make  certain  assumptions 
as  to  the  current  distribution  in  the  conductors,  which  we  know 
will  depend  upon  the  frequency  of  the  current  and  the  diameter 
of  the  conductors  themselves. 

If  we  write  equation  (2)  in  the  form 

L=  (£  +  0.46  Iogi0- 

we  may  assign  to  k  certain  values  found  to  agree  with  actual 
measurements  of  self-induction  under  various  working  conditions. 
With  stranded  cables  of  circular  section  insulated  for  5,000 
volts  working  pressure,  it  would  appear  that  average  values  of 
k  at  normal  frequencies  are  as  follows  : — 

SECTION  OF  CONDUCTOR  VAT  . 

IN  SQUARE  INCH. 

0.025  scl-  in>  -°7 

0.05        „  .05 

o.i  „  .035 

0-15         »  -025 

O.2  ,,  -  .02 

The  self-induction  of  large  cables  formed  of  cores  hammered 
to  clover  leaf  section  was  found  to  be  about  8  per  cent,  less  than 
the  corresponding  values  with  circular  cores. 

165 


APPENDIX    C 


ELECTROSTATIC    CAPACITY    OF    WIRES 

THE  Y  capacity  K1  per  mile  in  microfarads  of  each  conductor 
of  a  three-phase  overhead  line  is  given  approximately  by  the 
following  expression  :  — 

K       -°88 
1 


Where    d=  distance  between  centres  of  conductors. 

r=  radius  of  each  conductor,  r  and  d  being  expressed  in 
similar  units. 

In  the  case  of  overhead  lines,  however,  the  distance  the  wires 
are  from  the  ground  will  affect  the  electrostatic  capacity  of  the 
line  to  some  extent.  If  this  be  taken  into  account,  we  have  for 
the  Y  capacity  K,  per  mile  of  conductor  in  microfarads  :  — 

.0388 


Where  d  and  r  have  the  same  meaning  as  before  and  h  =  mean  height  of 
wires  above  ground  level,  r,  d,  and  h  being  expressed  in  similar 
units. 

It  was  seen  from  Fig.  8,  page  46,  that  the  electrostatic 
capacity  of  a  paper-insulated  E.H.P.  cable  increased  with  rise 
in  temperature.  The  capacity  will  also  vary  with  the  thickness 
and  quality  of  the  paper  dielectric  and  hence  with  the  working 
pressure  for  which  the  cable  is  constructed  ;  in  addition  it  will 
vary  with  the  section  of  the  conductors  themselves. 

166 


Electrostatic  Capacity  of  Wires 


167 


In  Fig.  80  curves  have  been  drawn  illustrating  the  variation 
in  Y  capacity  of  paper-insulated  three-phase  cables  constructed 

Y  Capacity  of  Three-Phase  E.S.C.  Cables. 


Y  Capacity,  Microfarads  per  Mile, 
p  o  o  o  T 

N  ^>  <jl  6)  0 

A 

\ 

B 

\\ 

C 

\ 
N 

s\ 

D 

\ 

X 

X 

x^ 

\ 

"X 

\ 

^ 

^= 

^^H 
^J 

^  . 

L^: 

""•^ 
•^  — 

•*^-^, 
-  —  », 
-^=^ 
~  _ 

-  — 

—  •  — 
•  —  — 
— 

—  —  , 
—  ^= 
—  — 
— 

-—  ~ 
•~  — 

•  ^, 

—  •  

4  8  12.  16  20 

Working  Pressure,  Kilovolts. 

=  o.2  sq.  in.         B  =  o.i5  scj.  in.         C=o.i  sq.  in.         D  —  .05  sq.  in. 
FIG.  80. 


with  Engineering  Standards  Committee's  thickness  of  dielectric 
for  various  sections  of  conductor  and  working  pressures. 


APPENDIX    D 


LINE    CALCULATIONS 

THE  solution  of  problems  relating  to  transmission  lines  and 
cables  carrying  alternating  currents  due  to  impressed  pressure 
waves  of  pure  sine  form  can  usually  be  effected  very  easily  by 
graphical  methods.  Such  methods  possess  the  advantage  also 
of  rendering  visible  to  the  eye  phase  relationship  and  its  changes 
due  to  reactance.  The  graphical  method,  however,  in  some 
cases  results  in  incommensurable  quantities,  some  lines  when 
drawn  to  scale  being  inconveniently  large  and  others  as  incon- 
veniently small.  An  analytical  method,  generally  known  as  the 
symbolic  method,  enables  calculations  regarding  the  most  com- 
plicated combinations  of  alternate  current  circuits  to  be  made 
with  as  much  ease  and  accuracy  as  by  simple  arithmetic. 

The  method  briefly  explained  involves  two  conventions  as 
follows  :  — 

(i)  We  know  that  the  resultant  of  any  number  of  pressures 
or  currents,  &c.,  may  be  found  from  a  vector  diagram  as  in  the 
case  of  forces.  The  vectors  may,  however,  be  combined  algebrai- 
cally by  adding  the  vertical  and  horizontal  components  of  each 
vector,  which  will  give  the  vertical  and  horizontal  components 
of  the  resultant.  To  indicate  that  one  set  of  components  are  at 
right  angles  to  the  initial  line  the  prefix  /'  is  used.  Thus  if  a 
voltage  is  given  by  the  equation  :  — 


it   is  represented   by  V  =  (R  +  zL/)A  in   Fig.   81.      If  the  co- 
efficient of  i  is   +  then  V  is  in  advance  of  A,  and  the  vector 
z'L/A  is  in  advance  of  the  vector  RA. 
Similarly,  if 


the  vector  AK  is  in  advance  of  the  vector  V  by  90°. 


Line  Calculations 


169 


(2)  If  we  choose  lines  along  and  perpendicular  to  OA  as 
axes  of  reference,  then  V  is  represented  by 

V  cos  4>  +  *  V  &in  $• 

If,  however,  our  lines  of  reference  are  the  axes  ox  and  oy,  and 
if  the  components  of  A  upon  these  axes  are  respectively  a  and  b, 
then  the  components  of  V  are  given  by  : — 
V-[R+*X>]  [«+#]. 
Thus  if  we  treat  i2  as  =  —  I  we  get 

V  =  [«R  - b\.p\  +  i  [£R  +  aLp\ 

As  an  example  of  the  application  of  this  method  we  may 
take  the  case  of  a  three-phase  inductive  load  requiring  a  constant 


FIG.  81. 


pressure  of  20,000  volts  between  phases  fed  through  a  5o-mile 
length  of  .05  sq.  in.  three-core  cable. 

Assume — 

Frequency  of  supply,  50  periods. 

Power  factor  of  load  =  0.8. 

Load  current,  40  amperes  per  phase. 

For    a    5O-mile  length    of   .05    sq.    in.    three-core    20,000- 
volt  cable  we  may  take  : — 

Resistance  per  core  =      42.95  ohms. 

Inductance  (zip)  per  core        =      11.75      „ 
Y  capacity  per  core  =      IO-55  microfarads. 

Power  factor  of  cable      -         =          .028. 


1 70  Three-Phase  Transmission 

All  three  voltages  and  currents  being  equal,  and  the 
potentials  of  the  system  symmetrical  with  regard  to  earth,  the 
problem  reduces  itself  to  a  single-phase  load  of  known  power 
factor  and  constant  pressure,  fed  through  a  single  conductor  of 
known  resistance,  self-induction,  and  capacity  by  a  single-phase 
generator  whose  voltage  is  required,  the  circuit  being  com- 
pleted through  an  imaginary  earth  return  of  resistance,  &c.,  zero. 

It  will  be  sufficiently  accurate  for  most  practical  purposes  to 
consider  the  total  capacity  as  bunched  in  the  middle  of  the  line 


FIG.  82. 

Our  circuit  may  now  be  represented  diagrammatically  by 
Fig.  82,  in  which  the  values  of  our  constants  are  as  follows  :  — 

20000 

VL  =  —  j=-  =  11,550  volts. 

r=  21.47  ohms. 
27r«/=5.87  ohms. 

K=  10.55  microfarads. 
A  =  40  amperes. 
Cos  <£  =  0.8. 

Starting  with  the  required  voltage  at  the  load  and  working 
backwards  towards  the  generator  we  have  :— 


,=  11550  (cos 
=  11550  (0.8  +  /.  0.6) 
=  9240  +  6930  .  i. 


=  859  +  235  .  /. 
'.  V=  10.099  +  7*65  .  /. 


Line  Calculations  171 

Now  AK  =  K^  = 

of 

and  taking  n  =  50  periods, 


Hence  AK  =  .00331  .  /  [10.099  +  7l^5  • 


So  far  we  have  taken  no  account  of  the  dielectric  loss  in  the 
cable.  With  the  assumed  power  factor  of  the  cable  .028  we 
must  add  to  the  above  value  of  AK  a  current  :  — 

.028  x  .oo33iV  =  .936  +  .665  .  /'. 
Our  value  of  AK  is  now 

—  22.76  +  34.06  .  /. 
Now  A,-,  =  AK  +  A 

=  I  7.  3  4-  34-06.  /. 
And  as      VG  -  V  =  (/-  +  *.  27m/)  A,; 

=  [21.47  +  5.87  ./]  [17.3  +  34.06.*] 
=  172  +  833.*. 
Therefore        V,;  =  10.27  1  +  799§  •  i- 

We  have  now  obtained  the  components  of  the  vectors  repre- 
senting the  various  voltages  and  currents,  and  the  length  of 
each  vector  is  at  once  arrived  at  by  taking  the  square  root  of 
the  sum  of  the  squares  of  its  components. 

Thus  VG 


=  13,020  volts. 

Similarly  AG  =  38.  2  amperes. 

Similarly  V  =  1  2,390  volts. 

Again  the  tangent  of  the  angle  each  vector  makes  with  the 
initial  line  is  given  by  the  ratio  of  the  vertical  to  the  horizontal 
components. 

Thus  for  VG        tan  <fr  =    7998  =.?79  and  ^  =  38°  nearly. 
10,271 

The  power  due  to  a  voltage  and  a  current  vector  is  given 
in  watts  by  adding  the  product  of  their  respective  horizontal 
components  to  the  product  of  their  vertical  components. 

Thus  the  power  due  to  V,;  and  AG  is  — 

10,271  x  17.3  +  7998  x  34.06  =  450.2  kw.  per  phase, 
and  the  power  factor  =  cos  25°  =  .906. 

Proceeding  after  the  manner  indicated  above,  a  number  of 
results  have  been  worked  out  and  are  plotted  in  the  curves 
given  by  Fig.  n,  which  relate  to  a  three-phase  transmission 
under  the  working  conditions  assumed. 


APPENDIX    E 


COMPARISON    OF    TRANSMISSION    SYSTEMS 

WE  have  seen  from  Chapter  III.  that  in  transmitting  a  certain 
amount  of  power  with  three-phase  cables  over  a  given  distance, 
the  sectional  area  of  the  conductors  or  the  amount  of  copper 
required  will  vary  inversely  as  the  square  of  the  pressure 
employed  for  the  same  loss  in  the  line.  A  similar  result  may 
be  shown  to  be  true  generally  with  all  transmission  systems. 
As,  however,  different  potentials  will  often  occur  between  parts 
of  the  same  transmission  system,  it  becomes  of  importance  in 
making  any  comparison  to  arrive  at  definite  pressure  relations 
with  regard  to  each  system  as  a  basis  for  such  comparison. 
Thus  the  amount  of  copper  required  to  transmit  a  definite 
amount  of  power  over  a  given  distance,  and  with  a  fixed  loss 
in  the  line,  by  any  particular  system,  may  be  considered  on  the 
basis  of  equal  maximum  pressures  between  any  parts  of  the 
system,  or,  on  the  other  hand,  that  of  equal  maximum  pressure 
between  any  parts  of  the  system  and  earth.  Further,  the 
minimum  pressures  between  the  branches  of  each  system  may 
be  taken  as  a  basis  for  comparison. 

In  making  comparisons  between  direct  current  and  alternating 
current  systems,  it  is  also  to  be  noted  that  whilst  in  the  case  of 
the  direct  current  system  the  maximum  pressure  will  not  exceed 
the  working  pressure  between  parts  of  the  system,  yet  in  the 
case  of  alternating  current  systems  the  maximum  pressure  will 
be  \/2  times  as  great  as  the  effective  working  pressure  between 
the  same  parts  of  the  system.  The  continuous  current  system 
would,  therefore,  on  the  basis  of  equal  maximum  pressure,  only 
be  expected  to  require  half  the  amount  of  copper  as  the 
alternating  current  system. 

With  the  transmission  of  power  over  long  distances  the  most 
important  basis  for  the  comparison  of  the  different  systems  is 

172 


Comparison  of  Transmission  Systems     173 

the  maximum  potential,  which  will  occur  between  any  part  of 
the  system. 

Starting  with  the  single-phase  system  let 

e  =  effective  voltage  between  wires. 
c=  effective  current  per  wire. 
r=--  resistance  per  wire. 
Then  the  power  transmitted  =  ect 

and  the  line  loss  =  2c2r. 

With  a  two-phase  system  having  four  wires  we  have  two 
distinct  single-phase  circuits,  each  wire  carrying  half  the  current 
and  having  twice  the  resistance  of  the  single-phase  conductors, 
the  amount  of  copper  required  will  be  the  same  for  equal 
loss  and  power  transmitted. 

In  the  case  of  a  two-phase  three-wire  system,  the  pressure 
between  each  outer  and  common  return  must  be  reduced  to 

—:-  to  maintain  the  same  maximum  pressure  e  between  wires, 

v  2 

the  current  in  each  outer  will  be    /-  and  in  the  common  return  c. 

If  we  denote  by  rv  the  resistance  of  each  outer,  the  total 
resistance  of  the  conductors  will  be 


and  the  total  loss 

o      (2  +    x/2) 
fr>\  -  ?—'  • 
2 

equating  this  to  the  loss  in  the  single-phase  system  we  find 


and  the  amount  of  copper  required  is  1.457  times  that  of  the 
single-phase  system. 

With   a    three-phase    system   employing   three   wires    with 
pressure  e  between  them  and  line  current  cv  we  have  : — 

Power  transmitted  =  ec^  \Aj. 
Line  loss  =  y\r\- 

Now,  since  ec-^  ^3  must  be  equal  to  the  power  of  the  single- 
phase  system  ec  ;  c^  =  — T=,  and  the  total  loss  will  be  &r^  as  com- 


174 


Three-Phase  Transmission 


pared  with  a  loss  of  2c-r  in  the  single-phase  system.  Hence, 
i\  =  2r,  and  the  amount  of  copper  required  in  each  three-phase 
line  is  only  half  of  that  in  each  single-phase  line.  The  total 
respective  weights  of  copper  will,  therefore,  be  as  f  to  2  or  f 
to  i.  That  is,  the  three-phase  system  will  only  require  three- 
quarters  of  the  copper  of  the  single-phase  system. 

Collecting  the  above  results  and  taking  the  weight  of  copper 
required  by  the  single-phase  circuit  as  100,  we  have  the  following 
relative  values : — 

TABLE   XXII. 


System. 

No.  of  Wires. 

Relative  Weight  of 
Copper. 

Two-  Phase  - 

3 

145-7 

Two-  Phase  - 

4 

100 

One-Phase  - 

2 

IOO 

Three-Phase 

3 

75 

Proceeding  as  before,  however,  we  may  compare  the  above 
systems  as  regards  the  same  maximum  potentials  to  earth,  in 
which  case  we  shall  find  some  considerable  differences,  as  will  be 
seen  from  the  following  table  : — 


TABLE   XXIII. 


System. 

No.  of  Wires; 

Relative  Weight  of 
Copper. 

One-Phase,  one  pole  earthed  - 

-7 

IOO 

Two-Phase,  one  pole  earthed  - 

4 

IOO 

Two-Phase,  common  return  earthed 
Three-Phase,  neutral  point  earthed 

3 
3 

72.8 
25 

INDEX 


ALL-DAY     efficiency     of     trans- 
formers, 10 
Alternate  current  generator,  commut- 

ating,  158 

Alternator  characteristic,  32 
Aluminium  conductors,  16 
Analysis  of  wave  forms,  113 
Andrews'  reverse  current  relay,  83 
Annual  losses  in  cables,  49 

—  transformation  loss,  1 1 

—  transmission  loss,  u 
A  poles,  strength  of,  142 

Area,  sectional,  most  economical,  40 
Arrangement  of  bus  bars,  70 

—  of  switchgear,  60 
Arresters,  lightning,  146 
Automatic  switches,  control  of,  75 
Auxiliary  bus  bars,  70 

Average  current  throughout  year,  10 

—  effective  current,  1 8 


BOARD  of  Trade  regulations,  28, 
161 

Boosters,  induction  type,  15 
Boosting,  29 

—  example  of,  1 60 

—  financial  considerations,  30,  158 
Bus  bars,  arrangement  of,  70 

—  bars,  auxiliary,  70 


CABLES,  E.H.P.,  capacity,  20,  166 
—  E.H.P.,  charging  current,  13, 

20,  50,  51 
—  E.H.P.,  copper  losses,  17,  47 


Cables,  E.H.P.,  cost  of,  33,  39,  45 

—  E.H.P.,  dielectric  losses,  17,  47,  52 

—  E.H.P.,  field  surrounding,  25 

—  E.H.P.,  financial  considerations,  4 
-  E.H.P.,  impedance,  92,  95 

—  E.H.P.,  in  parallel,  74 

—  E.H.P.,  power  factor,  21 

—  E.H.P.,  protection  from  lightning, 

134 

—  E.H.P.,  sectional  area,  40 

—  E.H.P.,  self-induction,  165 

—  E.H.P.,  temperature  test,  46 
Calculations,  line,  168 
Capacity  current  calculation,  20 

—  current,  copper  loss,  21 

—  and  impedance,  12 
Characteristic  of  alternator,  32 
Coils,  induction  or  choke,  147 

—  solenoid  trip,  77 
Companies,  power  distribution,  2 
Comparison  of  transmission  systems, 

172 

Competition,  9  • 

Concentration  of  potential,  109 
Conductors,  overhead  line,  16 
Consent  for  overhead  line,  163 
Converter,  rotary,  158 
Corona  effect,  u,  54 
Correction  of  power  factor,  1 50 
Critical  voltage,  54 

—  voltage,  Kapp's  formula,  55 
Cross  arms,  strength  of,  143 
Current,  average  effective,  10,  18 

—  effect  on  power  surges,  13 

—  reverse,  relays,  84 

—  transformer,  76,  89 


Index 


Current,  triple  frequency,  129 
—  working  limits,  13 
Curves  of  lighting  load,  10 


D 'ALTON,  P.  W.,  on  cable  power- 
factor,  21 
Dielectric  as  electrolyte,  52 

—  energy,  loss  in,  18,  21,  47 

—  resistance,  19 

—  strength,  53 

Discrimination  between  relays,  81 
Dispersion,  atmospheric,  55 
Distortion  of  wave  by  capacity,  121 
Drop  in  pressure,  reactive,  1 5 

EARTHING,  123,  129,  133 
Economical  span,  143 
Economies  in  working,  35 
Effective  capacity  of  cables,  20 

—  current  average,  10,  18 
Effect  of  low  power  factor,  157 
Efficiency,  all-day,  10 

—  of  transmission,  43 
Electrostatic  capacity  of  cables,  166 
Element,  inverse  time,  75 

Energy  of  circuit,  electromagnetic  and 

electrostatic,  104 
Extensions,  financial  considerations,  5 

ACTOR  load,  10 

power,  21,  150,  157 
Feeders  in  parallel,  75 
Ferranti  oil  switch,  72 
-  relay,  77 

—  switchgear,  63 

Field,  M.  B.,  on  potential  of  systems, 
124 

—  surrounding  cable,  25 
Fir  poles,  strength  of,  141 
Frame  metal,  switchboards,  65 
Frequency,  fundamental,  resonance  at, 

100 

—  indicator,  97 

—  natural  oscillations,  97 

—  triple,  currents,  129 
Fuse  time  element,  77 


/"^ENERAL   wave,  expression    for, 

O         n9 

Generator,  A.C.,  commutating,  158 

—  motor,  substations,  82 

—  voltage  regulation,  1 5 
Grouping  of  relays,  80 

HARMONICS,  elimination  of,  117 
—  resonance  with,  99 

—  rotation  of,  1 1 8 

—  triple  frequency,  117 
Height  of  wires,  137,  161 

High  pressure  transformers,  135 


T  MPEDANCE  of  three-  and  four- 
-L         core  cables,  92,  95 

—  to  triple  frequency  currents,  99 
Indicator,  frequency,  97 
Induction  booster,  30 

—  motor,  recent  improvements,  158 

—  self,  of  wires  and  cables,  93,  165 
Insulators,  suspension  type,  12 
Inverse  time  element,  75 
Iron-clad  switchgear,  67 


K 


APP,  critical  voltage  formula,  55 
Kelvin's  law,  13,  37. 


LEAD  sheath  losses,  23 
Leakage  effect  on  potential,  125 
Leakage  safety  devices,  136 
Life  of  plant  and  mains,  5 
Lightning  arresters,  146 

—  protection  from,  16 
Limit  of  working  current,  1 3 

—  of  working  pressure,  12 
Line  calculations,  168 

—  overhead  capacity,  166 

—  overhead  potential,  131 

—  overhead     regulations,     Board    of 

Trade,  28,  40,  161 

—  overhead  self-induction,  165 

—  overhead  supports,  137 

—  overhead  technical  considerations, 

ii 

—  regulation  of  pressure,  58 


Index 


177 


Linking  up  power  stations,  2 
Load  curves,  lighting,  10 
—  factor,  10 

Loans,  public  repayment  of,  6 
Losses,  transmission,  17 
Low  power  factor,  157 


MAINS,  potential  of  125 
—  protection  from  lighting,  134 
Mains,  underground,  i 
Maximum  working  pressure,  2 
Mechanical  analogy  resonance,  96 
Merz- Price  protective  gear,  70,  88 
Metal  frame  switchboards,  65 
Motor  induction  recent  improvements. 

158 
—  synchronous,  31,  82,  154 


NEUTRAL  point  earthing,  20,  80, 
128 
—  point  stability,  128 


/^VJJSOLESCENCE,  8 

v_X     Oerlikon  Co.  switcher  gear,  60, 

72 

Oerlikon  Co.  transformer,  135 
Oil  switches,  71 
Overhead  line,  conductors,  16 

—  line,  consents,  163 

—  line,  technical  features,  1 1 


T)ARALLEL  cables,  74 
A        Poles,  "A  "  type,  142 
Poles,  fir,  strength  of,  141 
Polyphase  relays,  81 
Potential,  concentration  of,  109 

—  of  mains,  125 

—  of  neutral  point,  128 

—  of  transmission  line,  131 

—  transformer,  85 
Power  companies,  2 

—  factor  of  cable,  2 1 

—  factor  correction,  1 50 

—  factor,  effect  of,  151 


Power  relays,  85 

—  stations,  linking  up,  2 

—  stations,  parallel  working,  9 

—  surges,  13,  103 

—  transformers,  E.H. P.,  135 
Pressure  drop  on  line,  15 

—  maximum  working,  2,  12 
-  regulation,  29,  33 

—  rise,  cause  of,  96 

—  rise  with  resonance,  98 

—  wind,  on  wires,  139 
Protection  from  lightning,  134 


REACTANCE,  capacity  and  self- 
induction,  IO2 
Reflected  wave,  106 

—  resonance,  108 
Regulation  pressure,  29 

—  synchronous  motor,  31 
Relay  calibration  curves,  78 

—  disc  synchronous  speed,  78 

—  function  of,  76 

—  grouping,  80 

—  reverse,  83,  85 
Resonance,  96 

—  at  fundamental  frequency,  100 

—  with  harmonics,  99 

Ring  type  current  transformer,  89 
Rise  of  pressure,  98 
Rotary  converters,  158 


SAFETY  devices,  leakage,  134 
Sag  of  overhead  wires,  139 
Sectional  area  most  economical,  40 
Self-induction  of  wires  and  cables,  165 
Solenoid  relay,  76 
Span,  economical,  143 
Stay  wires,  145 
Strength  of  fir  poles,  141 
Substation  switchboards,  64 
Supplementary  supply,  9 
Surges,  power,  13,  103 
Suspension  type  insulator,  12 
Switchboard  construction,  59 
Switches,  oil  break,  72 
Switching  on  and  off  cables,  36 


Index 


Synchronous  motor,  154 

—  substations,  82 

—  speed  of  relay  disc,  78 

TECHNICAL    features,    overhead  | 
lines,  ii 

Telephones,  145 

Temperature  test  of  E.H.P.  cable,  46 
Thompson,  Sylvanus,  reverse  relay,  85  | 
Time  element  fuse,  77 
Transformer,  current,  76 

—  efficiency,  all-day,  10 

—  losses,  8 

—  potential,  85 

—  power,  E.H.P.,  135 

—  ring  type,  89 
Transmission  line,  potential,  131 

—  line  supports,  137 

—  losses,  17 

—  schemes,  3 

—  systems,  comparison,  172 
Trip  coils,  solenoid,  77 


Triple  frequency  currents,  99,  130 
Trunk  mains,  i 


USEFUL  power  from  synchronous 
motor,  157 


T  i  WATTMETER  type  relay,  85 

W       Wave  analysis,  113 
Wave  distortion  by  capacity,  121 

—  equation  to,  1 1 1 

—  form,  1 10 

—  form  factor,  116 

—  form  general  expression,  119 

—  form  variation,  116 

—  reflected,  106 
Wind  pressure,  139 

Wires,  overhead,  capacity,  166 

—  overhead,  sag,  139 

—  overhead,  self-induction,  165 

—  overhead,  stays  for,  145 

—  overhead,  weight  and  tension,  139 


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ise on  the  theory  and  practice  of  the  mechanical  equipment  of  power 
stations  for  electric  supply  and  for  electric  traction.  Second  Edition,  revised. 
Illustrated.  8vo.,  cloth,  700  pp Net,  $5.00 

CHILD,  CHAS.  T.  The  How  and  Why  of  Electricity:  a  book  of  information  for 
non-technical  readers,  treating  of  the  properties  of  Electricity,  and  how 
it  is  generated,  handled,  controlled,  measured,  and  set  to  work.  Also 
explaining  the  operation  of  Electrical  Apparatus.  Illustrated.  8vo., 
cloth,  140  pp $1  00 

CLARK,  D.  K.  Tramways,  Their  Construction  and  Working.  Second  Edition. 
Illustrated.  8vo.,  cloth,  758  pp $9.00 

COOPER,  W.  R.  Primary  Batteries:  their  Theory,  Construction,  and  Use.  131 
Illustrations.  8vo.,  cloth,  324  pp Net,  $4.00 

The  Electrician  Primers.  Being  a  series  of  helpful  primers  on  electrical 
subjects,  for  the  use  of  students,  pupils,  artisans,  and  general  readers. 
Second  Edition.  Illustrated.  Three  volumes  in  one.  8vo. ,  cloth,  Net,  $5.00 

Vol.  I.— Theory Net,  $2 .00 

Vol.  II. — Electric  Traction,  Lighting  and  Power Net,  $3.00 

Vol.  III. — Telegraphy,  Telephony,  etc Net,  $2 .00 

CROCKER,  F.  B.     Electric  Lighting.     A  Practical  Exposition  of  the  Art  for  the 

use  of  Electricians,  Students,  and  others  interested  in  the  Installation  or 

Operation  of  Electric-Lighting  Plants. 
Vol.  I.— The  Generating  Plant.     Sixth  Edition,  entirely  revised.      Illustrated. 

8vo.,  cloth,  482  pp $3.00 

Vol.  II. — Distributing  System  and  Lamps.     Sixth  Edition.     Illustrated.     8vo., 

cloth,  505  pp $3.00 

and  ARENDT,  M.     Electric  Motors:    Their  Action,  Control,  and  Application. 

160  Illustrations.    8vo.,  cloth,  296  pp Net,  2.50 

and  WHEELER,  S.  S.     The  Management  of  Electrical  Machinery.     Being  a 

thoroughly  revised  and  rewritten  edition  of  the  authors'  "Practical  Manage- 
ment of  Dynamos  and  Motors."  Eighth  Edition.  Illustrated.  16mo., 
cloth,  232  pp Net,  $1 .00 

GUSHING,  H.  C.,  Jr.  Standard  Wiring  for  Electric  Light  and  Power.  Illustrated. 
16mo.,  leather,  156  pp $1 .00 

DAVIES,  F.  H.  Electric  Power  and  Traction.  Illustrated.  8vo.,  cloth,  293  pp 
(Van  Nostrand's  Westminster  Series.) Net,  $2 . 00 

DAWSON,  PHILIP.  Electric  Traction  on  Railways.  610  Illustrations.  8vo., 
half  leather,  891  pp Net,  $9.00 

DEL  MAR,  W.  A.    Electric  Power  Conductors.   69  illustrations.    8vo.,  cloth,  330  pp. 

Net,  $2.00 

DINGER,  Lieut.  H.  C.  Handbook  for  the  Care  and  Operation  of  Naval  Machinery. 
Second  Edition.  Illustrated.  16mo.,  cloth,  302  pp Net,  $2 .00 


4  LIST  OF  WORKS  ON  ELECTRICAL  SCIENCE 

DYNAMIC  ELECTRICITY;  Its  Modern  Use  and  Measurement, chiefly,  in  its  appli- 
cation to  Electric  Lighting  and  Telegraphy,  including:  1.  Some  Points  in 
Electric  Lighting,  by  Dr.  John  Hopkinson.  2.  On  the  Treatment  of  Elec- 
tricity for  Commercial  Purposes,  by  J.  N.  Shoolbred.  3.  Electric-Light 
Arithmetic,  by  R.  E.  Day,  M.E.  Fourth  Edition.  Illustrated.  IGmo.. 
boards,  166  pp.  (No.  71  Van  Nostrand's  Science  Series.) 50  cents 

EDGCUMBE,  K.  Industrial  Electrical  Measuring  Instruments.  Illustrated.  8vo., 
cloth,  227  pp Net,  $2.50 

ERSKINE-MURRAY,  J.  A  Handbook  of  Wireless  Telegraphy:  Its  Theory  and 
Practice.  For  the  use  of  electrical  engineers,  students,  and  operators. 
Second  Edition,  revised  and  enlarged.  180  illustrations.  8vo.,  cloth,  388 
pp Net,  $3.0) 

Wireless  Telephones  and  How  they  Work.     Illustrated.     16mo.,  cloth,  75  pp. 

$1.00 

EWING,  J.  A.  Magnetic  Induction  in  Iron  and  other  Metals.  Third  Edition,  revised. 
Illustrated.  8vo.,  cloth,  393  pp Net  $4.00 

FISHER,  H.  K.  C.,  and  DARBY,  W.  C.  Students'  Guide  to  Submarine  Cable  Test- 
ing. Third  Edition,  enlarged.  Illus.  8vo.,  cloth,  326  pp Net,  $3 . 50 

FLEMING,  J.  A.     The  Alternate-Current  Transformer  in  Theory  and  Practice. 
Vol.  I.:    The  Induction  of  Electric  Currents.     Fifth  Issue.     Illustrated.    8vb., 

cloth,  641  pp_ ' Net,  $5 .00 

Vol.   II.:    The  Utilization   of   Induced   Currents.     Third   Issue.     Illustrated. 

8vo,  cloth,  587  pp Net,  $5.00 

Handbook  for  the  Electrical  Laboratory  and  Testing  Room.     Two  Volumes. 
Illustrated.    8vo.,  cloth,  1160  pp.     Each  vol Net,  $5.00 

FOSTER,  H.  A.  With  the  Collaboration  of  Eminent  Specialists.  Electrical  Engi- 
neers' Pocket  Book.'  A  handbook  of  useful  data  for  Electricians  and 
Electrical  Engineers.  With  innumerable  Tables,  Diagrams,  and  Figures. 
The  most  complete  book  of  its  kind  ever  published,  treating  of  the  latest 
and  best  Practice  in  Electrical  Engineering.  Fifth  Edition,  completely 
revised  and  enlarged.  Fully  Illustrated.  Pocket  Size.  Leather.  Thumb 
Indexed.  1636  pp $5.00 

FOWLE,  F.  F.  The  Protection  of  Railroads  from  Overhead  Transmission  Line 
Crossings.  35  illustrations.  12mo  ,  cloth,  76  pp Net,  $1 . 50 

GANT,  L.  W.  Elements  of  Electric  Traction  for  Motormen  and  Others.  Illustrated 
with  Diagrams.  8vo.,  cloth,  217  pp Net,  $2 . 50 

GERHARDI,  C.  H.  W.  Electricity  Meters;  their  Construction  and  Management. 
A  practical  manual  for  central  station  engineers,  distribution  engineers 
and  students.  Illustrated.  8vo.,  cloth,  337  pp Net,  $-1 .00 


LIST  OF  JVORKS  ON  ELECTRICAL  SCIENCE.  5 

GORE,  GEORGE.  The  Art  of  Electrolytic  Separation  of  Metals  (Theoretical  and 
Practical).  Illustrated.  8vo.,  cloth,  295  pp Net,  $3.50 

GRAY,  J.  Electrical  Influence  Machines:  Their  Historical  Development  and 
Modern  Forms.  With  Instructions  for  making  them.  Second  Edition, 
revised  and  enlarged.  With  105  Figures  and  Diagrams.  12mo.,  cloth, 
296  pp $2.00 

GROTH,  L.  A.  Welding  and  Cutting  Metals  by  Aid  of  Gases  or  Electricity.  124 
illustrations.  8vo.,  cloth,  280  pp , Net,  $3 .00 

HAMMER,  W.  J.  Radium,  and  Other  Radio-Active  Substances;  Polonium,  Actin- 
ium, and  Thorium.  With  a  consideration  of  Phosphorescent  and  Fluo- 
rescent Substances,  the  properties  and  applications  of  Selenium,  and  the 
treatment  of  disease  by  the  Ultra- Violet  Light.  With  Engravings  and 
Plates.  Svo.,  cloth,  72  pp $1.00 

HARRISON,  N.  Electric  Wiring  Diagrams  and  Switchboards.  Illustrated.  12mo., 
cloth,  272  pp $1 .50 

HASKINS,  C.  H.     The  Galvanometer  and  its  Uses.     A  Manual  for  Electricians 

and  Students.     Fifth  Edition,  revised.     Illus.     16mo.,  morocco.  75pp.  .$1 .50 

HAY,  ALFRED.  Principles  of  Alternate-Current  Working.  Second  Edition. 
Illustrated.  12mo.,  cloth,  390  pp $2.00 

Alternating  ^Currents;    their   theory,   generation,  and   transformation.    Second 
Edition.     1 178  Illustrations.     8vo.,  cloth,  319  pp Net,  $2 . 50 

An  Introductory    Course    of    Continuous-Current    Engineering.       Illustrated. 
8vo.,   cloth,  327  pp Net,  $2.50 

HEAVISIDE,  0.  Electromagnetic  Theory.  Two  Volumes  with  Many  Diagrams. 
8vo.,  cloth,  1008  pp.  Each  vol Net,  $5.00 

HEDGES,  K.  Modern  Lightning  Conductors.  An  illustrated  Supplement  to  the 
Report  of  the  Research  Committee  of  1905,  with  notes  as  to  methods  of 
protection  and  specifications.  Illustrated.  8vo.,  cloth,  119  pp.  .Net,  $3 .00 

HOBART,  H.  M.  Heavy  Electrical  Engineering.  Illustrated.  8vo.,  cloth,  338 
pp Net,  $4.50 

Electricity.      A  text-book  designed  in  particular  for  engineering  students. 

115  illustrations.     43  tables.     8vo.,  cloth,  266  pp Net,  $2.00 

HOBBS,  W.  R.  P.  The  Arithmetic  of  Electrical  Measurements.  With  numerous 
examples,  fully  worked.  Twelfth  Edition.  12mo.,  cloth  126  pp..  .50  cents 

HOMANS,  J.  E.  A  B  C  of  the  Telephone.  With  269  Illustrations.  12mo., 
cloth,  352  pp $1 .00 

HOPKINS,  N.  M.  Experimental  Electrochemistry,  Theoretically  and  Practically 
Treated.  Profusely  illustrated  with  130  new  drawings,  diagrams,  and 
photographs,  accompanied  by  a  Bibliography.  Illustrated.  8vo.,  cloth, 
298  pp Net,  $3.00 


6  LIST  OF  WORKS  ON  ELECTRICAL  SCIENCE. 

HOUSTON,  EDWIN  J.  A  Dictionary  of  Electrical  Words,  Terms,  and  Phrases. 
Fourth  Edition,  rewritten  and  greatly  enlarged.  582  Illustrations.  4to., 

cloth Net,  $7.00 

A  Pocket  Dictionary  of  Electrical  Words,  Terms,  and  Phrases.  12mo.,  cloth, 
950  pp Net>  $2-50 

HUTCHINSON,  R.  W.,  Jr.  Long-Distance  Electric  Power  Transmission:  Being 
a  Treatise  on  the  Hydro-Electric  Generation  of  Energy;  Its  Transformation, 
Transmission,  and  Distribution.  Second  Edition.  Illustrated.  12mo., 
cloth,  350  pp Net,  $3.00 

and  IHLSENG,  M.  C.  Electricity  in  Mir-ing.  Being  a  theoretical  and  prac- 
tical treatise  on  the  construction,  operation,  and  maintenance  of  electrical 
mining  machinery.  Illustrated.  12mo.,  cloth In  Press 

INCANDESCENT  ELECTRIC  LIGHTING.  A  Practical  Description  of  the  Edison 
System,  by  H.  Latimer.  To  which  is  added:  The  Design  and  Operation  of 
Incandescent  Stations,  by  C.  J.  Field;  A  Description  of  the  Edison  Electro- 
lyte Meter,  by  A.  E.  Kennelly;  and  a  Paper  on  the  Maximum  Efficiency  of 
Incandescent  Lamps,  by  T.  W.  Howell.  Fifth  Edition.  Illustrated. 
16mo.,  cloth,  140  pp.  (No.  57  Van  Nostrand's  Science  Series.) 50  cents 

INDUCTION  COILS:  How  Made  and  How  Used.  Eleventh  Edition.  Illustrated. 
16mo.,  cloth,  123  pp.  (No.  53  Van  Nostrand's  Science  Series.). .  .50  cents 

JEHL,  FRANCIS.  The  Manufacture  of  Carbons  for  Electric  Lighting  and  Other 
Purposes.  Illustrated.  8vo  ,  cloth,  232  pp Net,  $4.00 

JONES,  HARRY  C.     The  Electrical  Nature  of  Matter  and  Radioactivity.     Second 
Edition,  completely  revised.     12mo.,  cloth,  212  pp $2.00 

KAPP,  GISBERT.  Electric  Transmission  of  Energy  and  its  Transformation, 
Subdivision,  and  Distribution.  A  Practical  Handbook.  Fourth  Edition, 
thoroughly  revised.  Illustrated.  12mo.,  cloth,  445  pp $3.50 

KAPP,  GISBERT.     Alternate-Current  Machinery.      Illustrated.      16mo.,     cloth, 

190  pp.     (No.  96  Van  Nostrand's  Science  Series.) 50  cents 

Dynamos,  Alternators,  and  Transformers.  Illustrated.  8vo.,  cloth,  507 
pp $4.00 

KELSEY,  W.  R.  Continuous-Current  Dynamos  and  Motors,  and  their  Control; 
being  a  series  of  articles  reprinted  from  the  "Practical  Engineer,"  and  com- 
pleted by  W  R.  Kelsey,  B.Sc.  With  Tables,  Figures,  and  Diagrams.  8vo., 
cloth,  439  pp $2.50 

KEMPE,     H.     R.      A     Handbook     of     Electrical     Testing.      Seventh     Edition, 

revised  and  enlarged.     285  Illustrations.     8vo..  cloth,  706  pp Net,  $6.00 

KENNEDY,    R.     Modern    Engines    and    Power    Generators.     Illustrated.     4to., 

Electrical   Installations   of   Electric    Light,  Power,   and   Traction    Machinery. 

Illustrated.    8vo.,  cloth,  5  vols.     The  Set,  $15.00 Each,  $3 . 50 


LIST  OF  WORKS  ON  ELECTRICAL  SCIENCE.  7 

KENNELLY,  A.  E.  Theoretical  Elements  of  Electro-Dynamic  Machinery.  Vol  I. 
Illustrated.  8vo.,  cloth,  90  pp $1 .50 

KERSHAW,  J.  B.  C.  The  Electric  Furnace  in  Iron  and  Steel  Production.  Illus- 
trated. 8vo.,  cloth,  74  pp Net,  $1 .50 

Electrometallurgy.     Illustrated.     8vo.,  cloth,  303  pp.     (Van  Nostrand's  West- 
minster Series.) Net,  $2 . 00 

KINZBRUNNER,  C.  Continuous-Current  Armatures;  their  Winding  and  Con- 
struction. 79  Illustrations.  8vo.,  cloth,  80  pp Net,  $1 .50 

Alternate-Current  Windings;    their  Theory  and  Construction.     89  Illustrations. 
8vo.,  cloth,  80  pp Net,  $1 .50 

KOE1TER,  F.  Hydroelectric  Developments  and  Engineering.  A  practical  and 
theoretical  treatise  on  the  development,  design,  construction,  equipment  aud 
operation  of  hydroelectric  transmission  plants.  500  illustrations.  4to., 

cloth,  475  pp Net,  $5.00 

—  Steam-Electric  Power  Plants.  A  practical  treatise  ou  the  design  of  central 
light  and  power  stations  and  their  economical  construction  and  operation. 
Fully  Illustrated.  4to.,  cloth,  455  pp  Net,  $5.00 

LARNER,  E.  T.  The  Principles  of  Alternating  Currents  for  Students  of  Electrical 
Engineering.  Illustrated  with  Diagrams.  12mo.,  cloth,  144  pp. Net,  $1.50 

LEMSTROM,  S.  Electricity  in  Agriculture  and  Horticulture.  Illustrated.  8vo., 
cloth Net,  $1 . 50 

LIVERMORE,  V.  P.,  and  WILLIAMS,  J.  How  to  Become  a  Competent  Motorman : 
Being  a  practical  treatise  on  the  proper  method  of  operating  a  street-railway 
motor-car;  also  giving  details  how  to  overcome  certain  defects.  Second 
Edition.  Illustrated.  16mo.,  cloth,  247  pp Net,  $1 .00 

LOCKWOOD,  T.  D.  Electricity,  Magnetism,  and  Electro-Telegraphy.  A  Prac- 
tical Guide  and  Handbook  of  General  Information  for  Electrical  Students, 
Operators,  and  Inspectors.  Fourth  Edition.  Illustrated.  8vo.,  cloth, 
374  pp $2.50 

LODGE,  OLIVER  J.  Signalling  Across  Space  Without  Wires :  Being  a  description 
of  the  work  of  Hertz  and  his  successors.  Fourth  Edition.  Illustrated.  8vo., 
cloth,  156  pp Net,  $2.00 

LORING,  A.  E.  A  Handbook  of  the  Electro-Magnetic  Telegraph.  Fourth  Edition, 
revised.  Illustrated.  16mo.,  cloth,  116  pp.  (No.  39  Van  Nostrand's 
Science  Series.) 50  cents 

LUPTON,  A.  PARR,  G.  D.  A.,  and  PERKIN,  H.  Electricity  Applied  to  Mining. 
Second  Edition.  With  Tables,  Diagrams,  and  Folding  Plates.  8vo..  cloth, 
320  pp Net,  $4.50 

MAILLOUX,     C.     0.     Electric     Traction     Machinery.     Illustrated.     8vo.,     cloth. 

In  Press 


8  LIST  OF  WORKS  ON  ELECTRICAL  SCIENCE. 

MANSFIELD,  A.  K.  Electromagnets:  Their  Design  and  Construction.  Second 
Edition.  Illustrated.  IGmo.,  cloth,  155  pp.  (Van  Nostrand's  Science 
Series  No.  64.) 50  cents 

MASSIE,  W.  W.,  and  UNDERBILL,  C.  R.  Wireless  Telegraphy  and  Telephony 
Popularly  Explained.  Illustrated.  12mo.,  cloth.  82  pp Net,  $1 .00 

MAURICE,  W.  Electrical  Blasting  Apparatus  and  Explosives,  with  special  refer- 
ence to  colliery  practice.  Illustrated.  8vo.,  cloth,  167  pp Net,  $3.50 

MONCKTON,  C.  C.  F.  Radio  Telegraphy.  173  Illustrations.  Svo.,  cloth,  272  pp. 
(Van  Nostrand's  Westminster  Series.) Net,  $2.00 

MORGAN,  ALFRED  P.  Wireless  Telegraph  Construction  for  Amateurs.  153  illus- 
trations. 12mo.,  cloth,  220  pp Net,  $1.50 

NIPHER,  FRANCIS  E.  Theory  of  Magnetic  Measurements.  With  an  Appendix 
on  the  Method  of  Least  Squares.  Illustrated.  12mo.,  cloth,  94  pp .  .  . $1 . 00 

NOLL,  AUGUSTUS.  How  to  Wire  Buildings.  A  Manual  of  the  Art  of  Interior 
Wiring.  Fourth  Edition.  Illustrated.  12mo.,  cloth,  165  pp $1 .50 

OHM,  G.  S.  The  Galvanic  Circuit  Investigated  Mathematically.  Berlin,  1827. 
Translated  by  William  Francis.  With  Preface  and  Notes  by  the  Editor, 
Thos.  D.  Lockwood.  Second  Edition.  Illustrated.  16mo.,  cloth,  269  pp. 
(No.  102  Van  Nostrand's  Science  Series.) • 50  cents 

OLSSON,  ANDREW.  Motor  Control  as  Used  in  Connection  with  Turret  Turning  and 
Gun  Elevating  (The  Ward  Leonard  System.)  13  illustrations.  12mo., 
paper,  27  pp.  (U.  S.  Navy  Electrical  Series  No.  1.) Net,  .50 

OUDIN,  MAURICE  A.  Standard  Polyphase  Apparatus  and  Systems.  Illustrated 
with  many  Photo-reproductions,  Diagrams,  and  Tables.  Fifth  Edition,  revised. 
Svo.,  cloth,  369  pp Net,  $3.00 

PALAZ,  A.  Treatise  on  Industrial  Photometry.  Specially  applied  to  Electric 
Lighting.  Translated  from  the  French  by  G.  W.  Patterson,  Jr.,  Assistant 
Professor  of  Physics  in  the  University  of  Michigan,  and  M.  R.  Patterson, 
B.A.  Second  Edition.  Fully  Illustrated.  Svo. ,  cloth,  324  pp $4.00 

PARR,  G.  D.  A.  Electrical  Engineering  Measuring  Instruments  for  Commercial 
and  Laboratory  Purposes.  With  370  Diagrams  and  Engravings.  8vo., 
cloth,  328  pp • .Net,  $3.50 

PARSHALL,  H.  F.,  and  HOBART,  H.  M.  Armature  Windings  of  Electric  Machines. 
Third  Edition.  With  140  full-page  Plates,  65  Tables,  and  165  pages  of 

descriptive  letter-press.     4to.,  cloth,  300  pp $7.50 

Electric  Railway  Engineering.     With  437  Figures  and   Diagrams  and  many 
Tables.     4to.,  cloth,  475  pp Net,  $10.00 

Electric  Machine  Design.     Being  a  revised  and  enlarged  edition  of  "Electric 
Generators."     648  Illustrations.     4to,  half  morocco,  601  pp Net,  $12 . 50 


LIST  OF  WORKS  ON  ELECTRICAL  SCIENCE.  9 

PERRINE,  F.  A.  C.  Conductors  for  Electrical  Distribution:  Their  Manufacture 
and  Materials,  the  Calculation  of  Circuits,  Pole-Line  Construction,  Under- 
ground Working,  and  other  Uses.  Second  Edition.  Illustrated.  8vo., 
cloth,  287  pp Net,  $3.50 

POPE,  F.  L.  Modern  Practice  of  the  Electric  Telegraph.  A  Handbook  for  Elec- 
tricians and  Operators.  Seventeenth  Edition.  Illustrated.  8vo.,  cloth, 
234  pp $1 .50 

RAPHAEL,  F.  C.  Localization  of  Faults  in  Electric-Light  Mains.  Second  Edition, 
revised.  Illustrated.  8vo.,  cloth,  205  pp Net,  $3.00 

RAYMOND,  E.  B.  Alternating-Current  Engineering,  Practically  Treated.  Third 
Edition,  revised.  With  many  Figures  and  Diagrams.  8vo.,  cloth,  244  pp., 

Net,  $2.50 

RICHARDSON,  S.  S.  Magnetism  and  Electricity  and  the  Principles  of  Electrical 
Measurement.  254  illustrations.  12mo.,  cloth,  604  pp Net,  $2.00 

ROBERTS,  J.  Laboratory  Work  in  Electrical  Engineering — Preliminary  Grade. 
A  series  of  laboratory  experiments  for  first-  and  second-year  students  in 
electrical  engineering.  Illustrated  with  many  Diagrams.  8vo.,  cloth, 
218  pp Net,  $2.00 

RUHMER,  ERNST.  Wireless  Telephony  in  Theory  and  Practice.  Translated 
from  the  German  by  James  Erskine-Murray.  Illustrated.  8vo.,  cloth, 
224  pp : Net,  $3.50 

RUSSELL,  A.  The  Theory  of  Electric  Cables  and  Networks.  71  Illustrations. 
8vo.,  cloth,  275  pp Net,  $3 .00 

SALOMONS,  DAVID.  Electric-Light  Installations.  A  Practical  Handbook.  Illus- 
trated. 12mo.,  cloth. 

Vol  I. :    Management  of  Accumulators.     Ninth  Edition.     178  pp $2 . 50 

Vol.  II. :    Apparatus.     Seventh  Edition.     318  pp $2 . 25 

Vol.  III.:    Application.     Seventh  Edition.     234  pp $1 .50 

SEVER,  G.  F.  Electrical  Engineering  Experiments  and  Tests  on  Direct-Current 
Machinery.  Second  Edition,  enlarged.  With  Diagrams  and  Figures.  8vo., 
pamphlet,  75  pp Net,  $1 .00 

and  TOWNSEND,  F.     Laboratory  and  Factory  Tests  in  Electrical  Engineering. 

Second  Edition.     Illustrated.     8vo.,  cloth,  269  pp .Net,  $2.50 

SEWALL,   C.   H.     Wireless  Telegraphy.     With   Diagrams   and   Figures.     Second 

Edition,  corrected.     Illustrated.     8vo.,  cloth,  229  pp Net,  $2 . 00 

Lessons  in  Telegraphy.     Illustrated.     12mo.,  cloth,  104  pp Net,  $1 .00 

—  T.     Elements  of  Electrical  Engineering.     Third  Edition,  revised.    Illustrated. 
8vo.,  cloth,  444  pp $3.00 

The  Construction  of  Dynamos  (Alternating  and  Direct  Current).  A  Text- 
book for  students,  engineering  contractors,  and  electricians-in-charge. 
Illustrated.  8vo.,  cloth,  316  pp $3.00 


10  LIST  OF  WORKS  ON  ELECTRICAL  SCIENCE. 

SHELDON,  S.,  and  HAUSMANN.E.  Dynamo-Electric  Machinery :    Its  Construction, 

Design,  and  Operation. 

Vol.  I.:  Direct-Current  Machines.  Eighth  Edition,  completely  rewritten. 
Illustrated.  8vo.,  cloth,  281  pp Net,  $2 .50 

and  MASON,  H.     Alternating-Current  Machines :  Being  the  second  volume 

of  "Dynamo-Electric  Machinery;  its  Construction,  Design,  and  Opera- 
tion." With  many  Diagrams  and  Figures.  (Binding  uniform  with  Vol- 
ume I.)  Seventh  Edition,  reurritten.  8vo.,  cloth,  353  pp Net,  $2 . 50 

SLOANE,  T.  O'CONOR.     Standard  Electrical  Dictionary.     300  Illustrations.     12mo., 

cloth,  682  pp $3.00 

Elementary  Electrical  Calculations.  A  Manual  of  Simple  Engineering 
Mathematics,  covering  the  whole  field  of  Direct  Current  Calculations,  the 
basis  of  Alternating  Current  Mathematics,  Networks,  and  typical  cases  of 
Circuits,  with  Appendices  on  special  subjects.  8vo.,  cloth.  Illustrated. 
304  pp Net,  $2.00 

SNELL,  ALBION  T.  Electric  Motive  Power.  The  Transmission  and  Distribution 
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on  the  Applications  of  Electricity  to  Mining  Work.  Second  Edition. 
Illustrated.  8vo.,  cloth,  411  pp Net,  $4.00 

SODDY,  F.  Radio-Activity ;  an  Elementary  Treatise  from  the  Standpoint  of  the 
Disintegration  Theory.  Fully  Illustrated.  8vo.,  cloth,  214  pp.  .Net,  $3.00 

SOLOMON,  MAURICE.  Electric  Lamps.  Illustrated.  8vo.,  cloth.  (Van  Nos- 
trand's  Westminster  Series.) Net,  $2 . 00 

STEWART,  A.  Modern  Polyphase  Machinery.  Illustrated.  12mo.,  cloth,  29G 
pp Net,  $2.00 

SWINBURNE,  JAS.,  and  WORDINGHAM,  C.  H.  The  Measurement  of  Electric 
Currents.  Electrical  Measuring  Instruments.  Meters  for  Electrical  Energy. 
Edited,  with  Preface,  by  T.  Commerford  Martin.  Folding  Plate  and  Numer- 
ous Illustrations.  16mo.,  cloth,  241  pp.  (No.  109  Van  Nostrand's  Science 
Series.) 50  cents 

SWOOPE,  C.  WALTON.  Lessons  in  Practical  Electricity:  Principles,  Experi- 
ments, and  Arithmetical  Problems.  An  Elementary  Text-book.  Eleventh 
Edition,  enlarged  with  a  chapter  on  alternating  currents.  404  illustrations. 
12mo.,  cloth,  507  pp Net,  $2 . 00 

THOM,  C.,  and  JONES,  W.  H.  Telegraphic  Connections,  embracing  recent  methods 
in  Quadruplex  Telegraphy.  20  Colored  Plates.  8vo.,  cloth,  59  pp.  .$1 .50 

THOMPSON,  S.  P.,  Prof.  Dynamo-Electric  Machinery.  With  an  Introduction 
and  Notes  by  Frank  L.  Pope  and  H.  R.  Butler.  Fully  Illustrated.  16mo., 

cloth,  214  pp.     (No.  66  Van  Nostrand's  Science  Series.) 50  cents 

Recent  Progress  in  Dynamo-Electric  Machines.  Being  a  Supplement  to 
"Dynamo-Electric  Machinery."  Illustrated.  16mo.,  cloth,  113  pp.  (No. 
75  Van  Nostrand's  Science  Series.) .50  cents 


LIST  OF   WORKS  ON  ELECTRICAL  SCIENCE.  11 

TOWNSEND,  FITZHUGH.  Alternating  Current  Engineering.  Illustrated.  8vo., 
paper,  32  pp Net,  75  cents 

UNDERBILL,  C.  R.  Solenoids,  Electromagnets  and  Electromagnetic  Windings. 
218  Illustrations.  12mo.,  cloth,  345  pp Net,  $2.00 

URQUHART,  J.  W.  Dynamo  Construction.  A  Practical  Handbook  for  the  use 
of  Engineer  Constructors  and  Electricians  in  Charge.  Illustrated.  12mo.. 
cloth $3.00 

Electric  Ship-Lighting.  A  Handbook  on  the  Practical  Fitting  and  Running  of 
Ship's  Electrical  Plant,  for  the  use  of  Ship  Owners  and  Builders,  Marine 
Electricians,  and  Sea-going  Engineers  in  Charge.  88  Illustrations.  12mo., 
cloth,  308  pp $3 .00 

Electric-Light  Fitting.  A  Handbook  for  Working  Electrical  Engineers,  em- 
bodying Practical  Notes  on  Installation  Management.  Second  Edition. 
With  numerous  Illustrations.  12mo.,  cloth $2 .00 

Electroplating.    Fifth  Edition.     Illustrated.     12mo.,  cloth,  230  pp $2.00 

Electrotyping.     Illustrated.     12mo.,  cloth,  228  pp $2 .00 

WADE,  E.  J.  Secondary  Batteries:  Their  Theory,  Construction,  and  Use.  Second 
Edition,  corrected.  265  illustrations.  8vo,  cloth,  501  pp Net,  $4.00 

WADSWORTH,  C.     Electric  Ignition.     15  Illustrations.     16mo.     paper.     In  Press 

WALKER,  FREDERICK.  Practical  Dynamo-Building  for  Amateurs.  How  to 
Wind  for  any  Output.  Third  Edition.  Illustrated.  16mo.,  cloth,  104  pp. 
(No.  98  Van  Nostrand's  Science  Series.) 50  cents 

—  SYDNEY  F.  Electricity  in  Homes  and  Workshops.  A  Practical  Treatise  on 
Auxiliary  Electrical  Apparatus.  Fourth  Edition.  Illustrated.  12mo., 

cloth,  358  pp $2 . 00 

Electricity  in  Mining.     Illustrated.     8vo.,  cloth,  385  pp $3.50 

WALLING,  B.  T.,  Lieut.-Com.  U.S.N.,  and  MARTIN,  JULIUS.  Electrical  Installa- 
tions of  the  United  States  Navy.  With  many  Diagrams  and  Engravings. 
8vo.,  cloth,  648  pp $6 . 00 

WATT,    ALEXANDER.     Electroplating    and    Refining    of    Metals.    New   Edition, 

rewritten  by  Arnold  Philip.     Illustrated.     8vo.,  cloth,  677  pp.  .Net,  $4.50 

Electro-Metallurgy.     Fifteenth   Edition.     Illustrated.     12mo.,    cloth,    225    pp., 

$1.00 

WEBB,  H.  L.  A  Practical  Guide  to  the  Testing  of  Insulated  Wires  and  Cables. 
Fifth  Edition.  Illustrated.  12mo.,  cloth,  118  pp $1 .00 

WEEKS,  R.   W.     The  Design   of  Alternate-Current  Transformer.      New  Edition 

in  Press 


12  LIST  OF  WORKS  ON  ELECTRICAL  SCIENCE. 

WEYMOUTH,  F.  MARTEN.  Drum  Armatures  and  Commutators.  (Theory  and 
Practice.)  A  complete  treatise  on  the  theory  and  construction  of  drum- 
winding,  and  of  commutators  for  closed-coil  armatures,  together  with  a  full 
rdsume  of  some  of  the  principal  points  involved  in  their  design,  and  an 
exposition  of  armature  reactions  and  sparking.  Illustrated.  8vo.,  cloth, 
295 pp Net,  $3.00 

WILKINSON,  H.  D.  Submarine  Cable-Laying,  Repairing,  and  Testing.  New  Edition . 
Illustrated.  8vo.,  cloth In  Frets 

YOUNG,  J.  ELTON.  Electrical  Testing  for  Telegraph  Engineers.  Illustrated 
8vo.,  cloth,  264  pp Net,  $4.00 

ZEIDLER,  J.  and  LUSTGARTEN,  J.  Electric  Arc  Lamps.  Their  principles,  con- 
struction and  working.  160  illustrations.  8vo.,  cloth,  200  pp Net,  $2.00 


A  96=page  Catalog  of  Books  on  Electricity,  classified  by 
subjects,  will  be  furnished  gratis,  postage  prepaid,  on 
application. 


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